Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 13–14 to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Unit Test Lessons 13–14 Answer Key
Describe in words the following expressions.
Question 1.
2x + 15
Answer:
Two times a number plus fifteen.
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
2x + 15
Two times a number plus fifteen.
Question 2.
5y – 12
Answer:
A number 5 times less twelve.
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
5y – 12
A number 5 times less twelve.
Solve for x.
Question 3.
x + 4 = 7
Answer:
x = 3
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 4 = 7
x = 7 – 4
x = 3
Question 4.
x + 8 = 124
Answer:
x = 116
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 8 = 124
x = 124 – 8
x = 116
Question 5.
x + 2 = 7
Answer:
x = 5
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 2 = 7
x = 7 – 2
x = 5
Question 6.
x + 9 = 14
Answer:
x = 5
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 9 = 14
x = 14 – 9
x = 5
Question 7.
x – 6 = 4
Answer:
x = 10
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 6 = 4
x = 4 + 6
x = 10
Question 8.
11x – 2 – 11x = -2
Answer:
Infinite
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
11x – 2 – 11x = -2
11x – 11x = -2 + 2
x = 0
Question 9.
x – 2 = 13
Answer:
x = 15
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 2 = 13
x = 13 + 2
x = 15
Question 10.
x – 5 = 9
Answer:
x = 14
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 5 = 9
x = 9 + 5
x = 14
Solve for y.
Question 11.
3y – 5 = 7
Answer:
y = 4
Explanation:
3y – 5 = 7
3y = 7 + 5
y = 12 ÷ 3
y = 4
Question 12.
2y + 3 = 11
Answer:
y = 4
Explanation:
2y + 3 = 11
2y = 11 – 3
y = 8 ÷ 2
y = 4
Question 13.
4y – 3 = 13
Answer:
y = 4
Explanation:
4y – 3 = 13
4y = 13 + 3
y = 16 ÷ 4
y = 4
Question 14.
2y – 7 = 9 + 2y
Answer:
No solution
Explanation:
2y – 7 = 9 + 2y
2y – 2y = 9 + 7
0 = 16
So, there is no solution.
Question 15.
6y – 6 = 18
Answer:
y = 4
Explanation:
6y – 6 = 18
6y = 18 + 6
y = 24 ÷ 6
y = 4
Question 16.
7y – 14 = 28
Answer:
y = 6
Explanation:
7y – 14 = 28
7y = 28 + 14
y = 42 ÷ 7
y = 6
Question 17.
6y + 26 = 56
Answer:
y = 5
Explanation:
6y + 26 = 56
6y = 56 – 26
y = 30 ÷ 6
y = 5
Question 18.
12y – 24 = 48
Answer:
y = 6
Explanation:
12y – 24 = 48
12y = 48 + 24
12y = 72
y = 72 ÷ 12
y = 6
Give the coordinates for each point.
Question 19.
A _____________
Answer:
A(1,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
A(1,1) is marked on the above cartesian plane x-axis and y-axis.
Question 20.
B _____________
Answer:
B(3,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
B(3,1) is marked on the above cartesian plane x-axis and y-axis.
Question 21.
C _____________
Answer:
C(-1,-3)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
C(-1, -3) is marked on the above cartesian plane x-axis and y-axis.
Question 22.
D _____________
Answer:
D(-1,2)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
D(-1,2) is marked on the above cartesian plane x-axis and y-axis.
Question 23.
E _____________
Answer:
E(-2,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
E(-2,1) is marked on the above cartesian plane x-axis and y-axis.
Question 24.
F _____________
Answer:
F(-3,-3)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
F(-3,-3) is marked on the above cartesian plane x-axis and y-axis.
Question 25.
G _____________
Answer:
G(4, -4)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis. The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
G(4, -4) is marked on the above cartesian plane x-axis and y-axis.
Question 26.
H _____________
Answer:
H(5, 5)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
H(5, 5) is marked on the above cartesian plane x-axis and y-axis.
Plot the following points on the grid.
Question 27.
Point A (6, 6)
Point B (-3, -3)
Point C (-1, 2)
Point D (3, -2)
Point E (4, -2)
Point F (-4, 2)
Point G (-6, -6)
Point H (-1, 3)
Answer:
Explanation:
Find the first number along the x-axis.
Put your finger on that spot and move your finger up and down in a vertical line,
then still you will be at the same x number.
To find the exact point you want, look at the second number.
It tells you where to move your finger along the vertical line.
The above diagram shows the following points as,
Point A (6, 6)
Point B (-3, -3)
Point C (-1, 2)
Point D (3, -2)
Point E (4, -2)
Point F (-4, 2)
Point G (-6, -6)
Point H (-1, 3)
Create a function table for 2x + 1 and plot the ordered pairs on the grid.
Question 28.
2x + 1
What is the slope of the line created?
Answer:
The slope is 2.
Explanation:
Create function table for each equation.
y = 2x + 1
x = 0, 1, 2, 3…
y = 2 x 0 + 1
y = 1
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y.
Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope.
Slope = rise/run
Slope = 2/1 = 2
Question 29.
If the function table above (for question 28) were changed to 2x + 3, what would happen to the slope of the line?
Answer:
The line shifts, but the slope is still 2.
Explanation:
Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope
Slope = rise/run
Slope = 2/1 = 2
Create function tables for 2x – 1 and x + 3.
Plot the ordered pairs and determine the value of x,
where the equation 2x – 1 = x + 3 is true.
Question 30.
2x – 1
x + 3
Answer:
Explanation:
Create function table for each equation as shown above.
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y.
Pot the two lines on a co-ordinate plane.
Visually assess the lines to determine the point of intersection.