Texas Go Math Grade 8 Module 5 Quiz Answer Key

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Texas Go Math Grade 8 Module 5 Quiz Answer Key

Texas Go Math Grade 8 Module 5 Ready to Go On? Answer Key

5.1 Writing Linear Equations from Situations and Graphs

Write the equation of each line in slope-intercept form.

Question 1.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 13
Answer:
The standard form of an equation for the linear function is y = mx + b. To write an equation in slope-intercept form, we need to get values for the slope and y-intercept.

We can read the starting point from the graph, which is the intersection on the y-axis when x = 0. So we can read what our value is for the y-intercept. → starting point is (0, b)
Thus, b = 20.

The slope is calculated by:
m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Choose two points from the graph and put them in thecalculation I’ll take (0, 20) for (x1, y1) and (2, 80) for (x2, y2)
m = \(\frac{80-20}{2-0}\)
m = \(\frac{60}{2}\)
m = 30
The equation in slope-intercept form is: y = 30x + 20

Question 2.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 2
Answer:
The standard form of an equation for the linear function is y = mx + b. To write an equation in slope-intercept form, we need to get values for the slope and y-intercept.

We can read the starting point from the graph, which is the intersection on the y-axis when x = 0. So we can read what our value is for the y-intercept. → starting point is (0, b)
Thus, b = 60

The slope is calculated by:
\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Choose two points from the graph and put them in the calculation (0, 60) for (x1, y1) and (6, 0) for (x2, y2)
m = \(\frac{0-60}{6-0}\)
m = \(\frac{-60}{6}\)
m = -10
The equation in slope-intercept form is: y = -10x + 60

5.2 Writing Linear Equations from a Table

Write the equation of each linear relationship in slope-intercept form.

Question 3.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 3
Answer:
The standard form of an equation for the linear function is y = mx + b. To write an equation in slope-intercept form, we need to get values for the slope and y-intercept.

We can read the starting point from the graph, which is the intersection on the y-axis when x = 0. So we can read what our value is for the y-intercept. → starting point is (0, b)
Thus, b = 1.5

The slope is calculated by:
\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Choose two points from the graph and put them in the calculation (0, 1.5) for (x1, y1) and (100, 36.5) for (x2, y2)
m = \(\frac{36.5-1.5}{100-0}\)
m = \(\frac{35}{100}\)
m = 0.35
The equation in slope-intercept form is: y = 0.35x + 1.5

Question 4.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 4
Answer:
The standard form of an equation for the linear function is y = mx + b. To write an equation in slope-intercept form, we need to get values for the slope and y-intercept.

The slope is calculated by:
\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Choose two points from the graph and put them in the calculation (25, 94) for (x1, y1) and (35, 88) for (x2, y2)
m = \(\frac{88-94}{35-25}\)
m = \(\frac{-6}{10}\)
m = -0.6
To find the y-intercept (b), we can include one point from the table and the value of the slope in the standard form of the equation. So:
y = mx + b
94 = -0.6 . 25 + b
94 = -15 + b
b = 94 + 15
b = 109

The equation in slope-intercept form is: y = 0.6x + 109

5.3 Linear Relationships and Bivariate Data

Write the equation of the line that connects each set of data points.

Question 5.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 5
Answer:
The standard form of an equation for the linear function is y = mx + b. To write an equation in slope-intercept form, we need to get values for the slope and y-intercept.

The slope is calculated by:
\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Choose two points from the graph and put them in the calculation (20, 40) for (x1, y1) and (50, 60) for (x2, y2)
m = \(\frac{60-40}{50-20}\)
m = \(\frac{20}{30}\)
m = \(\frac{2}{3}\)
m ≈ 0.67

To find the y-intercept (b), we can include one point from the table and the value of the slope in the standard form of the equation. So:
y = mx + b
40 = 0.67 . 20 + b
40 = 13.4 + b
b = 40 – 13.4
b ≈ 26.6
The equation in slope-intercept form is: y = 0.67x + 26.6

Question 6.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 6
Answer:
Texas Go Math Grade 8 Module 5 Quiz Answer Key 11
Confirm the points represents a linear relationship

Slope = \(\frac{50-65}{30-25}\) = \(\frac{-15}{5}\) = -3
Find the slope using given points from the table by Slope(m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) where
(x2, y2) = (30, 50) and (x1, y1) = (25, 65)
50 = -3(30) + b Substituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):
50 = -90 + b y = mx + b
b = 50 + 90 = 140
y = -3x + 140 Substitute the value of slope (m) and y intercept (b) in slope-intercept form: y = mx + b

Essential Question

Question 7.
Write a real-world situation that can be represented by a linear relationship.
Answer:

Texas Go Math Grade 8 Module 5 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
An hourglass is turned over with the top part filled with sand. After 3 minutes, there are 855 mm of sand in the top half. After 10 minutes, there are 750 mm of sand in the top half. Which equation represents this situation?
(A) y = 285x
(B) y = -10.5x + 900
(C) y = -15x + 900
(D) y = 75x
Answer:
(C) y = -15x + 900

Explanation:
(3, 855) Write the given information as ordered pair

(10, 750)

Slope = \(\frac{855-750}{3-10}\) = \(\frac{105}{-7}\) = -15 Find the slope using given points by Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

750 = -15(10) + b Substituting the value of slope (m) and (x, y) in the
750 = -15(10) + b slope intercept form to find y intercept (b):
750= -150 + b
b = 750 + 150 = 900y = mx + b
y = -15x + 900 Substitute the value of slope (m) and y intercept (b) in slope-intercept form:
y = mx + b

Question 2.
Which graph shows a linear relationship?
Texas Go Math Grade 8 Module 5 Quiz Answer Key 7
Answer:
Texas Go Math Grade 8 Module 5 Quiz Answer Key 12
Graph B represents the linear relationship The data appears to lie on a straight line

Question 3.
What are the slope and y-intercept of the relationship shown in the table?
Texas Go Math Grade 8 Module 5 Quiz Answer Key 8
(A) slope = 0.05, y-intercept = 1,500
(B) slope = 0.5, y-intercept = 1,500
(C) slope = 0.05, y-intercept = 2,000
(D) slope = 0.5, y-intercept = 2,000
Answer:
(C) slope = 0.05, y-intercept = 2,000

Explanation:
slope = \(\frac{3000-2500}{20000-10000}\) = \(\frac{500}{10000}\) = 0.05
Find the slope using given points from the table by Slope(m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) where (x2, y2) = (20000, 3000) and (x1, y1) = (10000, 2500)

3000 = 0.05(2000) + b Substituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):
3000 = 1000 + b y = mx + b
b = 3000 – 1000 = 2000

Gridded Response

Question 4.
Franklin’s faucet was leaking water, so he put a bucket underneath to catch the water. After a while, Franklin started keeping track of how much water was leaking. His data is in the table below.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 9
Predict how many gallons of water will have leaked if Franklin hasn’t stopped the leak after 14 hours.
Texas Go Math Grade 8 Module 5 Quiz Answer Key 10
10
Answer:

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