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 = \(\frac{-2-2}{1-1}\)
undefined
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