Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 4 Review Test to finish your assignments.

## Math in Focus Grade 8 Course 3 A Chapter 4 Review Test Answer Key

**Concepts and Skills**

**Find the slope of each line using the points indicated. Then write an equation for it.**

Question 1.

Answer:

By seeing the above graph we can say that the line passes through (0, 0) and (12,5)

slope = (5 – 0)/(12-0)

slope = 5/12

The line passes through the y-axis at the point (0, 0).

Thus m = 5/12 and y-intercept b is 0.

y = 5/12 x

Question 2.

Answer:

The line passes through the points (4, 0) and (0, 6).

Slope m = \(\frac{6-0}{0-4}\)

= \(\frac{6}{-4}\)

= –\(\frac{3}{2}\)

The line passes through the y-axis at the point (0, 6).

Thus m = –\(\frac{3}{2}\) and y-intercept b is 6.

y = –\(\frac{3}{2}\)x + 6

Question 3.

Answer:

The line passes through the points (2, 3) and (-8, 3).

Slope m = \(\frac{3-3}{-8-2}\)

= \(\frac{0}{-10}\)

= 0

The line passes through the y-axis at the point (0, 3).

Thus m = 0 and y-intercept b is 3.

y = 3

Question 4.

Answer:

The line passes through the points (1, 2) and (1, -2).

Slope m = \(\frac{-2-2}{1-1}\)

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**For each line, state its slope and its y-intercept.**

Question 5.

y = \(\frac{1}{2}\)x – 3

Answer:

The equation is in the form of y = mx + b

y = \(\frac{1}{2}\)x – 3

m = \(\frac{1}{2}\)

y-intercept = -3

Question 6.

y = -3x + 4

Answer:

The equation is in the form of y = mx + b

y = -3x + 4

m = -3 and

y-intercept = 4

**Write an equation of each line given its slope and its y-intercept.**

Question 7.

Slope, m = -4

y-intercept, b = –\(\frac{1}{3}\)

Answer:

Given,

Slope, m = -4

y-intercept, b = –\(\frac{1}{3}\)

y = -4x – \(\frac{1}{3}\)

Question 8.

Slope, m = \(\frac{2}{5}\)

y-intercept, b = 3

Answer:

Given,

Slope, m = \(\frac{2}{5}\)

y-intercept, b = 3

y = \(\frac{2}{5}\)x + 3

**Solve. Show your work.**

Question 9.

Write an equation of the line parallel to 5y = 3x + 12 that has a y-intercept of 2.

Answer:

Given,

5y = 3x + 12

y = \(\frac{3}{5}\)x + 12

y-intercept of 2

y = \(\frac{3}{5}\)x + 2

Question 10.

Write an equation of the line that has slope –\(\frac{1}{2}\) and passes through the point (-4, 5).

Answer:

Given,

slope m = –\(\frac{1}{2}\)

y-intercept = 5

The equation of the line is y = mx + b

y = –\(\frac{1}{2}\)x + 5

Question 11.

Write an equation of the line that passes through the point (-4, -4) and is parallel to 2y – x = -6.

Answer:

Given equation

2y – x = -6

2y = x – 6

y = \(\frac{1}{2}\)x – 3

the line that passes through the point (-4, -4)

y = \(\frac{1}{2}\)x – 4

Question 12.

Write an equation of the line that passes through the point (-4, -3) and is parallel to 4y – x = -16.

Answer:

Given equation

4y – x = -16

4y = x – 16

y = \(\frac{1}{4}\)x – 4

the line that passes through the point (-4, -3)

y = \(\frac{1}{4}\)x – 3

**Write an equation of the line that passes through each pair of points.**

Question 13.

(0, 0) and (7, 7)

Answer:

The line passes through the points (0, 0) and (7, 7).

Slope m = \(\frac{7-0}{7-0}\)

= \(\frac{7}{7}\)

= 1

The line passes through the y-axis at the point (0, 0).

Thus m = 1 and y-intercept b is 0.

y = x

Question 14.

(1, 2) and (4, 8)

Answer:

The line passes through the points (1, 2) and (4, 8).

Slope m = \(\frac{8-2}{4-1}\)

= \(\frac{6}{3}\)

= 2

Thus m = 2 and y-intercept b is 0.

y = 2x

**Use graph paper. Graph each linear equation. Use 1 grid square on both axes to represent 1 unit for the interval from -5 to 5.**

Question 15.

4y = -3x – 8

Answer:

Given the equation

4y = -3x – 8

y = –\(\frac{3}{4}\)x – 2

slope = –\(\frac{3}{4}\) and

y-intercept = -2

Question 16.

Slope = \(\frac{1}{3}\); (0, -2)

Answer:

Given,

Slope = \(\frac{1}{3}\); (0, -2)

The equation of the line is y = mx + b

Substitute the given slope and points in the equation.

The equation of the line is y = \(\frac{1}{3}\)x – 2

**Problem Solving**

**Solved Show your work.**

Question 17.

Landscaping Company A and Company B each charges a certain amount, C dollars, as consultation fee, plus a fixed hourly charge.

a) Find the amount each landscaping company charges as its consultation fee.

Answer: Company A charges $400 and Company B charges $200.

b) Which company charges a greater amount per hour?

Answer: Company A

Question 18.

The operator of a charter bus service charges a certain amount for a bus, plus per-passenger charge. The graph shows the total charges, C dollars, for carrying x passengers.

a) Find the vertical intercept and explain what information it gives about the situation.

Answer: The vertical intercept is 100

b) Find the slope of the graph and explain what information it gives about the situation.

Answer:

The line passes through the points (40, 400) and (0, 100)

y-intercept is 100.

y = (100 – 400)/(0 – 40)

y = -300/-40

y = 30/4

y = 30/4 x + 100