McGraw Hill Math

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 15.5 Area with Customary Units to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 15.5 Area with Customary Units

Exercises

CALCULATE

Question 1.
What is the area of the rectangle?

Answer:
30 square in.,

Explanation:
Given to find the area of the rectangle of length 6 in. width 5 in,
so area = 6 in. X 5 in. = 30 square in.

Question 2.
What is the area of the square?

Answer:
16 square miles,

Explanation:
Given to find the area of the square with sides 4 mi each is
area = 4 mi X 4 mi = 16 square miles.

Question 3.
What is the area of the triangle?

Answer:
6 square in,

Explanation:
Given to find the area of the triangle with base 3 in. height 4 in.
it is 1/2 X 3 in. X 4 in. = 6 square in.

Question 4.
What is the area of the square?

Answer:
36 square in,

Explanation:
Given to find the area of the square with side 6 in.
so area = 6 in. X 6 in. = 36 square in.

Question 5.
What is the area of the rectangle?

Answer:
45 square ft,

Explanation:
Given to find the area of the rectangle of length 9 ft width 5 ft,
so area = 9 ft X 5 ft = 45 square ft.

Question 6.
What is the area of the triangle?

Answer:
62.5 square in.,

Explanation:
Given to find the area of the triangle with base 25 in. height 5 in.
it is 1/2 X 25 in. X 5 in. = 62.5 square in.

Question 7.
What is the area of the square?

Answer:
9 square in,

Explanation:
Given to find the area of the square with side 3 in.
so area = 3 in. X 3 in. = 9 square in.

Question 8.
What is the area of the rectangle?

Answer:
60 square in.,

Explanation:
Given to find the area of the rectangle of length 8 in. width 7.5 in,
so area = 8 in. X 7.5 in. = 60 square in.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 15.4 Perimeter with Customary Units to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 15.4 Perimeter with Customary Units

Exercises

CALCULATE

Question 1.
What is the perimeter of the figure shown?

Answer:
20 in.,

Explanation:
The perimeter of the figure shown with sides is
4 in, 6 in, 4 in, 6 in is 4 in + 6 in + 4 in + 6 in = 20 in.

Question 2.
What is the perimeter of the figure shown?

Answer:
26 in.,

Explanation:
The perimeter of the figure shown with sides is
7 in, 4 in, 6 in, 5 in, 4in is 7 in + 4 in + 6 in + 5 in + 4 in = 26 in.

Question 3.
What is the perimeter of the triangle?

Answer:
108 in.,

Explanation:
The perimeter of the figure shown with sides is
27 in, 36 in and 45 in is 27 in + 36 in + 45 in = 108 in.

Question 4.
What is the perimeter of the figure shown?

Answer:
44 in.,

Explanation:
The perimeter of the figure shown with sides is
12 in, 12 in, 10 in, 10 in is 12 in + 12 in + 10 in + 10 in = 44 in.

Question 5.
What is the perimeter of the figure shown?

Answer:
17 in.,

Explanation:
The perimeter of the figure shown with sides is
4 in, 6 in, 4 in, 3 in is 4 in + 6 in + 4 in + 3 in = 17 in.

Question 6.
What is the perimeter of the figure shown?

Answer:
36 ft,

Explanation:
The perimeter of the figure shown with sides is
four time 5 ft, 2 ft and 2 ft is 4 X (5 ft + 2 ft + 2 ft) = 4 X 9 ft = 36 ft.

Question 7.
Jane created the odd-shaped wheel pictured in the figure. If she were to push the wheel 3 times around, how far would she have pushed the wheel?

Answer:
81 ft,

Explanation:
Given Jane created the odd-shaped wheel
pictured in the figure as shown with 3 ft, 3ft, 3ft,
4 ft, 5 ft, 5 ft, 4 ft the perimeter of odd- shaped
wheel is 3 ft + 3 ft + 3 ft + 4 ft + 5 ft + 5 ft + 4 ft =
27 ft If she were to push the wheel 3 times around,
far would she have pushed the wheel is 3 X 27 ft = 81 ft.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 15.3 Customary Units of Weight to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 15.3 Customary Units of Weight

Exercises

CONVERT

Question 1.
86 oz = ____________ lb
Answer:
5.375 lb,

Explanation:
As 1 oz = 0.0625 lb, so 86 oz = 86 X 0.0625 lb = 5.375 lb.

Question 2.
8 lb 5 oz = _____________ oz
Answer:
133 oz,

Explanation:
As 1 lb = 16 oz, so 8 lb  = 8 X 16 oz = 128 oz,
128 oz + 5 oz = 133 oz.

Question 3.
10 T = ______________ lb
Answer:
22,046.2 lb,

Explanation:
As 1 T = 2,204.62 lb, so 10 T = 10 X 2,204.62 lb = 22,046.2 lb.

Question 4.
2400 lb = ______________ T
Answer:
1,088.621 T,

Explanation:
As 1 lb = 0.45359237 T, so 2,400 lb = 2,400 X 0.45359237 T = 1,088.621 T.

Question 5.
166 oz = _____________ lb
Answer:
10.375 lb,

Explanation:
As 1 oz = 0.0625 lb, so 166 oz = 166 X 0.0625 lb = 10.375 lb.

Question 6.
13 lb 6 oz = ________________ oz
Answer:
214 oz,

Explanation:
As 1 lb = 16 oz, so 13 lb  = 13 X 16 oz = 208 oz,
208 oz + 6 oz = 214 oz.

Question 7.
\(\frac{1}{4}\) T = ____________ lb
Answer:
551.155 lb,

Explanation:
As 1 T = 2,204.62 lb,
so \(\frac{1}{4}\) T = \(\frac{1}{4}\)  X 2,204.62 lb = 551.155 lb.

Question 8.
\(\frac{2}{5}\) T = ______________ lb
Answer:
881.848 lb,

Explanation:
As 1 T = 2,204.62 lb, so \(\frac{2}{5}\) T =
\(\frac{2}{5}\)  X 2,204.62 lb = 881.848 lb.

Question 9.
2 lb 12 oz + 2 lb 5 oz = ______________ oz
Answer:
81 oz,

Explanation:
As 1 lb = 16 oz, so 2 lb  = 2 X 16 oz = 32 oz,
32 oz + 12 oz = 44 oz and 2 lb 5 oz = 32 oz + 5 oz = 37 oz,
therefore 2 lb 12 oz + 2 lb 5 oz = 44 oz + 37 oz = 81 oz.

Question 10.
104 oz = ______________ lb
Answer:
6.5 lb,

Explanation:
As 1 oz = 0.0625 lb, so 104 oz = 166 X 0.0625 lb = 6.5 lb.

Question 11.
Barton’s backpack weighs 498 ounces. How many pounds does the backpack weigh?
Answer:
31.125 lb the backpack weigh,

Explanation:
Given Barton’s backpack weighs 498 ounces.
Number of pounds does the backpack weigh
as 1 oz = 0.0625 lb it is 498 X 0.0625 lb = 31.125 lb.

Question 12.
If Jason weighed 167 lb and he lost 112 oz during the summer, how much does he weigh after losing the weight?
Answer:
Jason weighs 2,560 oz after losing the weight,

Explanation:
Given If Jason weighed 167 lb and he lost 112 oz
during the summer, much does he weigh after losing the weight is
as 1 lb = 16 oz then 167 lb = 167 X 16 oz = 2,672 oz,
So it is 2,672 oz – 112 oz = 2,560 oz.

Question 13.
Kathleen weighed her two cats. The first cat weighed 7 lb 12 oz and the second weighed 11 lb 15 oz. How much did the two cats weigh in total?
Answer:
The two cats weigh in total is 315 oz,

Explanation:
Given Kathleen weighed her two cats.
The first cat weighed 7 lb 12 oz and the second weighed 11 lb 15 oz.
As 1 lb = 16 oz, first cat is 7 X 16 oz + 12 oz =
112 oz + 12 oz = 124 oz,
second cat is 11 X 16 oz + 15 oz = 176 oz + 15 oz = 191 oz,
So the two cats weigh in total is 124 oz + 191 oz = 315 oz.

Question 14.
Freddie’s camping gear weighs 70 lb in total. He adds an extra pair of shoes which weighs 2 lb 4 oz and removes tent stakes that weigh 6 lb 8 oz. How much does the gear weigh now?
Answer:
Gear weigh is 65.75 lb,

Explanation:
Given Freddie’s camping gear weighs 70 lb in total.
He adds an extra pair of shoes which weighs 2 lb 4 oz and
removes tent stakes that weigh 6 lb 8 oz.
So does the gear weigh now is as
1 oz = 0.0625 lb, 2 lb 4 oz = 2 lb + 4 X 0.625 lb =
2 lb + 0.25 lb = 2.25 lb,
so gear weigh + weigh of pair of shoes is
70 lb + 2.25 lb = 72.25 lb,
Now tent stakes weigh is 6 lb + 8 X 0.0625 lb =
6 lb + 0.5 lb = 6.5 lb, After removing tent stakes weighs
we get gear weigh as 72.25 lb – 6.5 lb = 65.75 lb.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 15.2 Customary Units of Liquid Volume to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 15.2 Customary Units of Liquid Volume

Exercises

CONVERT

Question 1.
72 c = ___________ qt
Answer:
18 qt,

Explanation:
As 1 cup = 0.25 quart, So 72 c = 18 qt.

Question 2.
12 qt = ____________ c
Answer:
48 c,

Explanation:
As 1 qt = 4 cups, So 12 qt = 48 c.

Question 3.
3 qt 1 pt = ____________ c
Answer:
5.99605 c,

Explanation:
As 1 qt = 1.66535 pt, So 3 qt = 4.99605 pt,
Therefore 3 qt 1 pt = 4.99605 pt + 1 pt = 5.99605 c.

Question 4.
192 gal = _____________ qt
Answer:
922.3296 qt,

Explanation:
As 1 gal = 4.8038 qt, So 192 gal = 192 X 4.8038 = 922.3296 qt.

Question 5.
328 qt = ____________ gal
Answer:
82 gal,

Explanation:
As 1 qt = 0.25 gal, So 328 qt = 82 gal.

Question 6.
2 gal 1 qt = _______________ c
Answer:
10.6076 c,

Explanation:
As 1 gal = 4.8038 qt, So 2 gal = 9.6076,
Therefore 2 gal 1 qt = 9.6076 + 1 = 10.6076 c.

Question 7.
6 qt 1 c = ____________ c
Answer:
25 c,

Explanation:
As 1 qt = 4 c, So 6 qt = 24 c,
Therefore 6 qt 1 c = 24 c + 1 c = 25 c.

Question 8.
52 c = _____________ qt
Answer:
13 qt,

Explanation:
As 1 c = 0.25 qt, So 52 c = 13 qt.

Question 9.
\(\frac{3}{4}\) gal = _____________ c
Answer:
12 c,

Explanation:
As 1 gal = 16 c, So \(\frac{3}{4}\) gal = 12 c.

Question 10.
66 pt = _______________ gal
Answer:
9.907854 gal,

Explanation:
As 1 pt = 0.150119 gal,
So 66 pt = 66 X 0.150119 = 9.907854 gal.

Question 11.
4 qt 1 c = _____________ c
Answer:
17 c,

Explanation:
As 1 qt = 4 c, So 4 qt = 16 c,
Therefore 4 qt 1 c = 16 c + 1 c = 17 c.

Question 12.
7\(\frac{1}{2}\) qt = _____________ gal = ___________ C
Answer:
1.875 gal, 30 c,

Explanation:
As 1 qt = 0.25 gal, So 7\(\frac{1}{2}\) qt = \(\frac{15}{2}\) qt = 1.875 gal. As 1 qt = 4 c,
So 7\(\frac{1}{2}\) qt = \(\frac{15}{2}\) qt =
7.5 X 4 = 30 c.

Question 13.
35 qt 3 c = ____________ gal
Answer:
9 gal,

Explanation:
As 1 qt = 4 c, So 35 qt = 140 c,
Therefore 35 qt 3 c = 140 c + 4 c = 144 c,
As we know 35 qt 3 c is 144 c, As 1 c = 0.0625 gal, So 144 c = 9 gal.

Question 14.
256 c = _______________ gal
Answer:
16 gal,

Explanation:
As 1 c = 0.0625 gal, So 256 c = 16 gal.

Question 15.
132 c = ___________ pt = ___________ qt
Answer:
4461.6 pt, 33 qt,

Explanation:
As 1 c = 33.8 pt, So 132 c = 4461.6 pt,
As 1 c = 0.25 qt, So 132 c = 33 qt.

Question 16.
34 gal 1 qt = ____________ pt
Answer:
273.6656 pt,

Explanation:
As 1 gal = 4.8038 qt, So 34 gal = 163.3292 qt,
Therefore 34 gal 1 qt = 163.3292 qt + 1 qt = 164.3292 qt
As we know 1 qt = 1.66535 pt, So 164.3292 qt = 273.6656.

Question 17.
Allison’s aquarium holds 25 gallons of water. One quart of water evaporated from the aquarium. How much water is left in the aquarium?
Answer:
119.095 quarts is left in the aquarium,

Explanation:
Given Allison’s aquarium holds 25 gallons of water.
One quart of water evaporated from the aquarium.
So water is left in the aquarium is as 1 gallon = 4.8038 quart,
25 gallons = 25 X 4.8038 quart = 120.095 quarts,
120.095 quarts – 1 quarts = 119.095 quarts.

Question 18.
Bobby drinks 1 quart and 1 cup of water for every 3 miles he runs. If he runs 9 miles, how much water should he drink?
Answer:
Bobby should drink 15 cups of water if he runs 9 miles,

Explanation:
Given Bobby drinks 1 quart and 1 cup of water for
every 3 miles he runs. As 1 quart = 4 cups, so
for 3 miles Bobby drinks 4 cups + 1 cup = 5 cups, So 1 mile it is 5/3 cups, therefore for 9 miles water should he drink is 5 X 9/3 = 15 cups.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 15.1 Customary Units of Length to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 15.1 Customary Units of Length

Exercises

CONVERT

Question 1.
72 in. = ____________ ft
Answer:
5.999976 ft,

Explanation:
As 1 inch = 0.083333 ft, So 72 in = 72 X 0.083333 = 5.999976 ft.

Question 2.
12 ft = _____________ in.
Answer:
144 in,

Explanation:
As 1 feet = 12 inches, So 12 ft = 12 X 12 = 144 inches,

Question 3.
3 ft 8 in. = ____________ in.
Answer:
44 inches,

Explanation:
As 1 ft = 12 inches, So 3 ft 8 in. = 3ft X 12 + 8 in. = 44 in.

Question 4.
192 in. = _______________ ft
Answer:
0.015999936 ft,

Explanation:
As 1 inch = 0.083333 ft, So 192 in. = 192 X 0.083333 = 0.015999936 ft.

Question 5.
7,920 ft = ______________ mi
Answer:
1.38068226 mi,

Explanation:
As 1ft = 0.000189394 mi, So 7,920 ft = 7,920 X 0.000189394 =
1.38068226 mi.

Question 6.
16 ft 6 in. = _______________ yd
Answer:
5.5 yd,

Explanation:
As 1 ft = 12 inches,
So 16 ft 6 in. = 16 ft X 12 + 6 = 198 in. 198 inches in yd,
As we know 1 in. = 0.0277778 yd, 198 inches = 198 X 0.0277778 = 5.5 yd.

Question 7.
4 ft 9 in. = ______________ in.
Answer:
57 in,
Explanation:
As 1 ft = 12 inches, So 4 ft 9 in. = 4ft X 12 + 9 = 57 in.

Question 8.
1056 ft = ______________ mi
Answer:
0.2 mi,

Explanation:
As 1ft = 0.000189394 mi, So 1056 ft. = 1056 X 0.000189394 = 0.2 mi.

Question 9.
\(\frac{4}{5}\)mi = ____________ in.
Answer:
50,688 in,

Explanation:
As 1 mi = 63,360 in, So \(\frac{4}{5}\)mi =
\(\frac{4}{5}\)mi X 63,360 = 50,688 in.

Question 10.
66 in. = _______________ ft
Answer:
5.499978 ft,

Explanation:
As 1 inches  = 0.083333 ft, So 66 in. = 66 in. X 0.083333 ft = 5.499978 ft.

Question 11.
648 in. = _____________ yd
Answer:
18 yd,

Explanation:
As 1 inches = 0.0277778 yd, So 648 in. = 648 in. X 0.0277778 yd = 18 yd.

Question 12.
7\(\frac{1}{2}\) yd = ____________ ft = __________ in.
Answer:
270 inches,

Explanation:
As 1 yd = 3 feet,
So 7\(\frac{1}{2}\)mi = \(\frac{15}{2}\)mi X 3 = 22.5 ft.
Now 1 ft = 12 inches, So 22.5 ft = 22.5 X 12 inches = 270 inches.

Question 13.
35 ft = ____________ yd
Answer:
11.666655 yd,

Explanation:
As 1ft = 0.333333 yd, So 35ft. = 35 ft X 0.333333 yd =11.666655 yd.

Question 14.
16 yd 2 ft = ____________ in.
Answer:
600 in,

Explanation:
As 1 yd = 3 ft, So 16 yd 2 ft = 16 yd X 3 + 2 = 50 ft,
50 ft in inches, As we know 1 ft = 12, So 50 ft = 50 ft X 12 = 600 in.

Question 15.
2 mi 303 yd = _______________ ft
Answer:
11,469 ft,

Explanation:
As 1 mi = 1,760 yd,
So 2 mi 303 yd = 2 X 1760 + 303 = 3,823 yd, 3,823 yd in ft,
As we know 1 yd = 3 ft, So 3,823 yd = 3,823 yd X 3 ft = 11,469 ft.

Question 16.
34 yd 2 ft = _____________ in.
Answer:
1,248 in,

Explanation:
As 1 yd = 3 ft, So 34 yd 2 ft = 34 X 3 + 2 = 104 ft,
104 ft in inches, As we know 1 ft = 12 inches,
So 104 ft = 104 X 12 = 1,248 in.

Question 17.
The river is 768 yards wide where the city plans to build a new bridge. How many 32-foot sections of bridge will the city engineers need in order to build the bridge?
Answer:
72 sections of 32 foot,

Explanation:
Given the river is 768 yards wide where the city plans to
build a new bridge. So 32-foot sections of bridge will the
city engineers need in order to build the bridge is as 1 yard = 3 feet,
so 768 yards = 768 X 3 feet = 2,304 feet, Therefore 32 foot sections are
2,304 feet ÷ 32 feet = 72 sections.

Question 18.
Patty wants to know how far she can throw a softball. After throwing, she estimates that the ball traveled 1,764 inches.
How many yards is that? ______________
How many feet? _______________
Answer:
The ball traveled 49 yd,
In feet the ball traveled 146.9999412 ft = 147 ft,

Explanation:
As 1 inch = 0.0277778 yd,
So  1,764 inches = 1764 X 0.0277778 yd = 49 yd.
As 1 inch = 0.0833333 ft, So 1,764 inches = 1,764 X 0.0833333 ft =
146.9999412 ft ≈ 147 ft.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 14.5 Graphing Relationships to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 14.5 Graphing Relationships

Exercises

Noah and Kim are making blue frosting for cupcakes. Kim adds 6 drops of blue food coloring to 1 cup of frosting and stirs until it is completely mixed. Noah adds 12 drops of blue food coloring to 2 cups of frosting and stirs until it is completely mixed. When they compare their two bowls, Noah is surprised to see that both frostings are the same shade of blue; he had expected his to be darker since he used more blue food coloring.

Question 1.
Explain why the two bowls of frosting are the same shade of blue.
Answer:
Both mixed same amount of quantity,

Explanation:
Given Noah and Kim are making blue frosting for cupcakes.
Kim adds 6 drops of blue food coloring to 1 cup of frosting and
stirs until it is completely mixed. Noah adds 12 drops of blue
food coloring to 2 cups of frosting and stirs until it is completely mixed.
When they compare their two bowls, Noah is surprised to see
that both frostings are the same shade of blue; he had expected
his to be darker since he used more blue food coloring.
But the two bowls of frosting are the same shade of blue because
both added 6 drops only to each cup.

Question 2.
What is the ratio (unit rate) of drops of food coloring to cups of frosting?
Answer:
6:1,

Explanation:
The ratio (unit rate) of drops of food coloring to cups of frosting as
it is 6 drops to 1 cup each it is 6:1.

Question 3.
Fill in the rest of the function table below for that ratio.

Answer:

Explanation:
Filled in the rest of the function table above for that ratio as shown above.

Question 4.
Plot the ordered pairs from the function table on the grid.

Answer:

Explanation:
Plotted the ordered pairs from the function table as (3,0.5),
(6,1), (9,1.5), (12,2) on the grid as shown above.

Question 5.
What is the slope of the line created?
Answer:
slope is \(\frac{1}{6}\),

Explanation:
A slope of a line is the change in y coordinate with respect to
the change in x coordinate The equation of the line is
written in the slope-intercept form, which is: y = mx + b,
where m represents the slope and b represents the y-intercept.
Therefore the given line y = x/6 has slope \(\frac{1}{6}\).

The chart below shows the speed of two cars in miles per hour.

Question 6.
Which car increased in speed more between 1:30 and 2:00? How do you know?
Answer:
Car A,

Explanation:
If we see speed of the cars between 1:30 and 2:00, Car A increased
from 35 miles to 45 miles and Car B is at constant speed of 35 miles only,
therefore Car A has increased the speed.

Question 7.
At what time do the cars begin to go different speeds?
Answer:
From 2:00 to 2:30,

Explanation:
From 2:00 to 2:30 Car A went with speed of 45 miles to
60 miles and Car B at speed of 35 miles to 45 miles,
So from 2:00 to 2:30 the cars begin to go different speeds.

Question 8.
Which car is going faster at 2:30?
Answer:
Car A,

Explanation:
At 2:30 Car A is at speed of 45 miles to 60 miles and
Car B at speed of 35 miles to 45 miles,
So if compare 45 miles > 35 miles therefore Car A is going faster.

Question 9.
Find the unit rate for the graph below.

Answer:
Unit rate is 10,

Explanation:
The unit rate, in the point represents the amount of vertical increase for every horizontal increase of unit on the graph.
Now if we see the given graph it has unit rate of  10/1 = 10, 20/2 = 10,
30/3 = 10, 40/4 = 10 and 50/5 = 10, It is constant 10.

Question 10.
Sketch a graph of a linear function that is negative and decreasing.

Answer:

Explanation:
If the graph goes down as it moves from left to right, then the graph depicts a decreasing function.
This is comparable to the side of a hill that is going downwards.

At x = 0, y = -3, if x = 1 , y = -2 even though the graph is
going up it is still a negative linear function because its
y values are negative.

Question 11.
Is the function above increasing or decreasing?
Answer:
Decreasing,

Explanation:
The slope comes out negative which confirms that the function is decreasing.

Question 12.
Is this function linear or nonlinear?

Answer:
Nonlinear,

Explanation:
The function is non linear as it is not a line.
Nonlinear Function – A function whose graph is not a line or part of a line.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 14.4 Slope to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 14.4 Slope

Exercises

FIND THE SLOPE

Question 1.

Answer:
\(\frac{5.6}{10}\),

Explanation:
Using two of the points on the line, we can find the slope of the line by
finding the rise and the run. The vertical change between two points is
called the rise and the horizontal change is called the run. The slope equals the rise divided by the run:
Slope =rise ÷ run = (y2 – y1) ÷ (x2 – x1),
We have given points as (-2, -5.1) and (8, 0.5),
So slope = (0.5 – (-5.1))/ (8 -(-2)) = 5.6/10.

Question 2.

Answer:
–\(\frac{8.1}{14}\),

Explanation:
Using two of the points on the line, we can find the slope of the line by
finding the rise and the run.
The vertical change between two points is called the rise and the horizontal change is called the run. The slope equals the rise divided by the run:
Slope =rise ÷ run = (y2 – y1) ÷ (x2 – x1),
We have given points as (-7, 7) and (7, -1.1),
So slope = (-1.1 – 7)/ (7 -(-7)) = -8.1/14.

Question 3.
y = 6x – 2
Answer:
Slope is 6,

Explanation:
A slope of a line is the change in y coordinate with respect to
the change in x coordinate. The equation of the line is written in the
slope-intercept form, which is: y = mx + b,
where m represents the slope and b represents the y-intercept.
Therefore the given line y = 6x – 2 has slope 6.

Question 4.
y – x = 4
Answer:
Slope is 1,

Explanation:
A slope of a line is the change in y coordinate with respect to
the change in x coordinate.
The equation of the line is written in the slope-intercept form,
which is: y = mx + b, where m represents the slope and b represents
the y-intercept. Therefore the given line y – x = 4, y = x + 4 has slope 1.

Question 5.
-3 = \(\frac{2}{3}\)x – y
Answer:
Slope is \(\frac{2}{3}\),

Explanation:
A slope of a line is the change in y coordinate with respect to
the change in x coordinate.
The equation of the line is written in the slope-intercept form,
which is: y = mx + b, where m represents the slope and
b represents the y-intercept.
Therefore the given line -3 = \(\frac{2}{3}\)x – y
y = \(\frac{2}{3}\)x + 3 has slope \(\frac{2}{3}\).

Question 6.
x + y = -5
Answer:
Slope is -1,

Explanation:
A slope of a line is the change in y coordinate with respect to
the change in x coordinate.
The equation of the line is written in the slope-intercept form,
which is: y = mx + b, where m represents the slope and b represents
the y-intercept.
Therefore the given line x + y = -5, y = -x – 5 = (-1)x – 5 has slope -1.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 14.3 Solve Equations by Graphing to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 14.3 Solve Equations by Graphing

Exercises

GRAPH

Determine the point of Intersection of the two lines.

Question 1.

y = x + 3

y = 2x + 1

Answer:

Explanation:
Determined the point of Intersection of the given two lines
1. y = x + 3, 2. y = 2x + 1,
1. y = x + 3, if x = -2, y =  -2 + 3 = 1,
if x = -1, y = -1 + 3 = 2, if x = 0, y = 0 + 3 = 3,
if x = 1, y = 1 + 3 = 4, if x = 2, y = 2 + 3 = 5,
if x = 3, y = 3 + 3 = 6.
2. y = 2x + 1, if x = -2, y =  2 X -2  + 1 = -4 + 1 = -3,
if x = -1, y = 2 X -1 + 1 = -2 + 1 = -1,
if x = 0, y = 2 X 0 + 1 = 0 + 1 = 1,
if x = 1, y = 2 X 1 + 1 = 2 + 1 = 3,
if x = 2, y = 2 X 2 + 1 = 4 + 1 = 5,
if x = 3, y = 2 X 3 + 1 = 6 + 1 = 7 as (2,5) as shown above.

Question 2.

y = x – 4

y = -x + 2

Answer:

Explanation:
Determined the point of Intersection of the given two lines
1. y = x – 4, 2. y = -x + 2,
1. y = x – 4, if x = -2, y =  -2 – 4 = -6, if x = -1, y = -1 – 4 = -5,
if x = 0, y = 0 – 4 = -4, if x = 1, y = 1 – 4 = -3,
if x = 2, y = 2 – 4 = -2, if x = 3, y = 3 – 4 = -1.
2. y =  -x + 2,
if x = -2, y =  -(-2) + 2 = 4, if x = -1, y = -(-1) + 2 = 3,
if x = 0, y = -0 + 2 = 2, if x = 1, y = -(1) + 2 = 1,
if x = 2, y = -(2) + 2 = 0, if x = 3, y = -(3) + 2 = -1
as (3,-1) as shown above.

Question 3.

y = 4x – 3

y = x

Answer:

Explanation:
Determined the point of Intersection of the given two lines
1. y = 4x – 3, 2. y = x,
1. y = 4x – 3, if x = -2, y =  4 X -2 – 3 = -11,
if x = -1, y = 4 X -1 – 3 = -7, if x = 0, y = 4 X 0 – 3 = -3,
if x = 1, y = 4 X 1 – 3 = 1, if x = 2, y = 4 X 2  – 3 = 5,
if x = 3, y = 4 X 3 – 3 = 9.
2. y = x, if x = -2, y = -2,
if x = -1, y = -1, if x = 0, y = 0,
if x = 1, y = 1, if x = 2, y = 2,
if x = 3, y = 3 as (1,1) as shown above.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 14.2 Function Tables to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 14.2 Function Tables

Exercises

CALCULATE

Fill in the corresponding values of y for the given x value in the function table.

Question 1.
y = x + 1

Answer:

Explanation:
Filled in the corresponding values of y for the given equation y = x + 1,
x value in the function table as  if x = 0 then y = 0 + 1 = 1,
if x = 1 then y = 1+1 = 2, if x = 2 then y = 2+ 1 = 3,
if x = 3 then y = 3 + 1 = 4, if x = 4 then y = 4 + 1 = 5 and
if x = 5 then y = 5 + 1 = 6 above.

Question 2.
y = 2x + 2

Answer:

Explanation:
Filled in the corresponding values of y for the given equation y = 2x + 2,
x value in the function table as if x = -2 then y = 2 X -2 + 2 = -4 + 2 = -2,
if x = -1 then y = 2 X -1 + 2 = -2 + 2 = 0,
if x = 0 then y = 2 X 0 + 2 = 0 + 2 = 2,
if x = 1 then y = 2 X 1 + 2 = 2 + 2 = 4,
if x =  2 then y = 2 X 2 + 2 = 4 + 2 = 6 and
if x = 3 then y = 2 X 3 + 2 = 6 + 2 = 8.

Question 3.
y = x – 4

Answer:

Explanation:
Filled in the corresponding values of y for the given equation y = x – 4,
x value in the function table as if x = 0 then y = 0 – 4 = -4,
if x = 1 then y = 1 – 4 = -3, if x = 4 then y = 4 – 4 = 0,
if x = 6 then y = 6 – 4 = 2, if x =  8 then y = 8 – 4 = 4 and
if x = 10 then y = 10 – 4 = 6.

Question 4.
y = 2x – 3

Answer:

Explanation:
Filled in the corresponding values of y for the given equation y = 2x – 3,
x value in the function table as
if x = -1 then y = 2 X -1 – 3 = -2 – 3 = -5,
if x = 0 then y = 2 X 0 – 3 = 0 – 3 = -3,
if x = 1 then y = 2 X 1 – 3 = 2 – 3 = -1,
if x = 2 then y = 2 X 2 – 3 = 4 – 3 = 1,
if x = 3 then y = 2 X 3 – 3 = 6 – 3 = 3 and
if x = 5 then y = 2 X 5 – 3 = 10 – 3 = 7.

Question 5.
y = 2x + 1

Answer:

Explanation:
Filled in the corresponding values of y for the given equation y = 2x + 1,
x value in the function table as
if x = -2 then y = 2 X -2 + 1 = -4 + 1 = -3,
if x = 1 then y = 2 X 1 + 1 = 2 + 1 = 3,
if x = 0 then y = 2 X 0 + 1 = 0 + 1 = 1,
if x = 2 then y = 2 X 2 + 1 = 4 + 1 = 5,
if x = 4 then y = 2 X 4 + 1 = 8 + 1 = 9 and
if x = 6 then y = 2 X 6 + 1 = 12 + 1 = 13.

Question 6.
y = \(\frac{1}{2}\)x + 1

Answer:

Explanation:
Filled in the corresponding values of y for the given equation
y = \(\frac{1}{2}\)x + 1, x value in the function table as
if x = -4 then y = \(\frac{1}{2}\) X -4 + 1= -2 + 1 = -1,
if x = -2 then y = \(\frac{1}{2}\) X -2 + 1 = 2 + 1 = 0,
if x = 0 then y = \(\frac{1}{2}\) X 0 + 1 = 0 + 1 = 1,
if x = 2 then y = \(\frac{1}{2}\) X 2 + 1 = 1 + 1 = 2,
if x = 4 then y = \(\frac{1}{2}\) X 4 + 1 = 2 + 1 = 3 and
if x = 6 then y = \(\frac{1}{2}\) X 6 + 1 = 3 + 1 = 4.

Identify the function by looking at the ordered pairs (x, y) in the function table.

Question 7.

Answer:
f(y) = x + 2,

Explanation:
If we see the values of y it is 2 more than x in each case,
therefore function of the ordered pairs is f(y) = x + 2.

Question 8.

Answer:
f(y) = 2x + 9,

Explanation:
If we see the values of y it is 2x and 9 more in each case,
therefore function of the ordered pairs is f(y) = 2x + 9.

Question 9.

Answer:
f(y) = x² + 2,

Explanation:
If we see the values of y it is square of x and 2 more in each case,
therefore function of the ordered pairs is f(y) = x + 2.

Question 10.

Answer:
f(y) = x³,

Explanation:
If we see the values of y it is cube of x,
therefore function of the ordered pairs is f(y) = x³.

Complete the function table and then graph the function.

Question 11.
y = 3x – 3

Answer:

Explanation:
Completed the function y = 3x – 3 in the table for values of
y for x value in the function table as
if x = -2 then y = 3 X -2 – 3 = -6 – 3 = -9,
if x = -1 then y = 3 X -1 – 3 = -3 – 3 = -6,
if x = 0 then y = 3 X 0 – 3 = 0 – 3 = -3,
if x = 1 then y = 3 X 1 – 3 = 3 – 3 = 0,
if x = 2 then y = 3 X 2 – 3 = 6 – 3 = 3 and
if x = 3 then y = 3 X 3 – 3 = 6.

Question 12.
y = x²

Answer:

Explanation:
Completed the function y = x² in the table for values of
y for x value in the function table as
if x = -3 then y = (-3)² = – 3 X – 3 = 9,
if x = -2 then y = (-2)² =  -2 X -2 = 4,
if x = -1 then y = (-1)² = -1 X -1 = 1,
if x = 0 then y = (0)² = 0 X 0 = 0,
if x = 1 then y = (1)² = 1 X 1 = 1,
if x = 2 then y = (2)² = 2 X 2 = 4 and
if x = 3 then y = (3)² = 3 X 3 = 6.

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 10 Lesson 8 Identifying Coins as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Answer Key Chapter 10 Lesson 8 Identifying Coins

Identify

Identify the Coin

Question 1.

Name _____________
Value _____________
Answer:
The name of the coin is dime
The value of the coin is $0.10 or 0.1 dollars

Question 2.

Name _____________
Value _____________
Answer:
The name of the coin is Washington quarter.
Value is 0.25 dollars or $0.25

Question 3.

Name _____________
Value _____________
Answer:
The name of the coin is penny
Value is 0.01 dollars or $0.01

Question 4.

Name _____________
Value _____________
Answer:
The name of the coin is Washington quarter.
Value is 0.25 dollars or $0.25