Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 4 Lesson 4.3 Writing Linear Equations to finish your assignments.
Math in Focus Grade 8 Course 3 A Chapter 4 Lesson 4.3 Answer Key Writing Linear Equations
Math in Focus Grade 8 Chapter 4 Lesson 4.3 Guided Practice Answer Key
For each line, state its slope and its y-intercept.
Question 1.
5x + 4y = 8
First, write the equation in the slope-intercept form.
5x + 4y = 8
5x + 4y – 
= 8 – Subtract 5x from both sides.
= Simplify.
= Divide both sides by .
y = Write in slope-intercept form.
Comparing the equation y = with y = mx + b:
Slope: m =
y-intercept: b =
Answer:
First, write the equation in the slope-intercept form.
5x + 4y = 8
5x + 4y – 5x = 8 – 5x Subtract 5x from both sides.
4y = 8 – 5x Simplify.
y = 2 – 5/4 x Divide both sides by 4.
y = -5/4 x + 2 Write in slope-intercept form.
Comparing the equation y = -5/4 x + 2 with y = mx + b:
Slope: m = -5/4
y-intercept: b = 2
Question 2.
2x – 3y = 7
First write the equation in the slope-intercept form.
2x – 3y = 7
2x – 3y + = 7 + Add 3y to both sides.
= Simplify.
= Subtract from both sides.
= Simplify.
= Divide both sides by .
y = Write in slope-intercept form.
Comparing the equation y = with y = mx + b:
Slope: m =
y-intercept: b =
Answer:
First write the equation in the slope-intercept form.
2x – 3y = 7
2x – 3y + 3y = 7 + 3y Add 3y to both sides.
2x = 7 + 3y Simplify.
2x – 2x = 7 + 3y – 2x Subtract 2x from both sides.
0 = 7 + 3y – 2x Simplify.
3y = 2x – 7 Divide both sides by 3.
y = 2/3 x – 7/3 Write in slope-intercept form.
Comparing the equation y = 2/3 x – 7/3 with y = mx + b:
Slope: m = 2/3
y-intercept: b = -7/3
Question 3.
5y – x = 15
Answer:
First write the equation in the slope-intercept form.
Add x on both sides
5y – x + x = 15 + x
5y = 15 + x
Subtract 5y on both sides
5y – 5y = 15 + x – 5y
0 = 15 + x – 5y
5y = x + 15
Divide by 5 on both sides
y = 1/5 x + 3
Question 4.
2y – 3x = -4
Answer:
First write the equation in the slope-intercept form.
2y = 3x -4
Divide by 2 on both sides
y = 3/2 x – 2
Question 5.
6y + 5x = 24
Answer:
First write the equation in the slope-intercept form.
Subtract 5x on both sides
6y + 5x – 5x = 24 – 5x
6y = 24 – 5x
Divide by 6 on both sides
y = 4 – 5x
y = -5x + 4
Question 6.
3y + 4x = 3
Answer:
First write the equation in the slope-intercept form.
Subtract 4x on both sides
3y + 4x -4x = 3 – 4x
3y = -4x + 3
Divide by 3 on both sides
y = -4/3 x + 1
Use the given slope and y-intercept of a line to write an equation in slope-intercept form.
Question 7.
Slope, m = –\(\frac{2}{3}\)
y-intercept, b = 4
y = mx + b
y = Substitute the given values for and b.
Answer:
y = mx + b
y = –\(\frac{2}{3}\) Substitute the given values for 4 and b.
Question 8.
Slope, m = 4
y-intercept, b = -7
Answer:
y = mx + b
y = 4 Substitute the given values for -7 and b.
Solve.
Question 9.
A line has the equation 3y + 6 = 10x. Write an equation of a line parallel to this given line that has a y-intercept of 2.
First write the given equation in slope-intercept form.
3y + 6 = 10x
3y + 6 – = 10x – Subtract both sides by 6.
= Simplify.
y = Divide both sides by .
y = Write in slope-intercept form.
The line has slope m = and y-intercept b = .
Then write an equation for the parallel line with slope m = and y-intercept b = .
y = . Substitute the values of m and b.
So, an equation of the line parallel to 3y = 10x – 6 is .
Answer:
First write the given equation in slope-intercept form.
3y + 6 = 10x
3y + 6 – 6 = 10x – 6 Subtract both sides by 6.
3y = 10x – 6 Simplify.
y = 10/3 x – 2 Divide both sides by 3.
y = 10/3 x – 2 Write in slope-intercept form.
The line has slope m = 10/3 and y-intercept b = -2.
Then write an equation for the parallel line with slope m = 10/3 and y-intercept b = -2
y = 10/3 x + 2. Substitute the values of m and b.
So, an equation of the line parallel to 3y = 10x – 6 is 10/3 x + 2.
Question 10.
A line has slope -3 and passes through the point (-6, 8). Write an equation of the line.
Answer:
Given,
A line has slope -3 and passes through the point (-6, 8)
m = -3
y-intercept = 8
y = -3x + 8
Question 11.
A line has slope \(\frac{1}{3}\) and passes through the point (0, 1). Write an equation of the line.
Answer:
Given,
A line has slope \(\frac{1}{3}\) and passes through the point (0, 1).
m = \(\frac{1}{3}\)
y-intercept = 1
y = mx + b
y = \(\frac{1}{3}\)x + 1
Question 12.
A line has slope 2 and passes through the point (1, 5). Write an equation of the line.
Answer:
Given,
A line has slope 2 and passes through the point (1, 5).
m = 2
y-intercept = 5
y = mx + b
y = 2x + 5
Question 13.
Write an equation of the line that passes through the point (-2, 1) and is parallel to y = 5 – 3x.
First, write the equation in slope-intercept form.
y = 5 – 3x
y = Write in slope-intercept form.
The line has slope m = .
So, the line parallel to y = 5 – 3x has slope m = .
Then use the slope m = . and the fact that (-2, 1) lies on the parallel line to find the y-intercept.
y = mx + b Write in slope-intercept form.
= Substitute the values for m, x, and y.
= Simplify.
= Subtract from both sides.
= Simplify.
The y-intercept is .
So, an equation of the line is .
Answer:
First, write the equation in slope-intercept form.
y = 5 – 3x
y = -3x + 5 Write in slope-intercept form.
The line has slope m = -2.
So, the line parallel to y = 5 – 3x has slope m = -3.
Then use the slope m = -2. and the fact that (-2, 1) lies on the parallel line to find the y-intercept.
y = mx + b Write in slope-intercept form.
y = -2x + 1 Substitute the values for m, x, and y.
So, an equation of the line is y = -2x + 1.
Question 14.
Write an equation of the line that passes through the pair of points (-2, -5) and (2, -1).
Answer:
The line passes through the points (-2, -5) and (2, -1).
Slope m = \(\frac{-1-(-5)}{2-(-2)}\)
= \(\frac{4}{4}\)
= 1
The line passes through the y-axis at the point (0, 0).
Thus m = 1 and y-intercept b is 0.
y = x
Math in Focus Course 3A Practice 4.3 Answer Key
Find the slope and the y-intercept of the graph of each equation.
Question 1.
y = -5x + 7
Answer:
Given,
y = -5x + 7
The equation of the line is y = mx + b
Slope, m = -4
y-intercept = 7
Question 2.
y = 2x + 3
Answer:
Given,
y = 2x + 3
The equation of the line is y = mx + b
Slope, m = 2
y-intercept = 3
Question 3.
5x + 2y = 6
Answer:
Given,
5x + 2y = 6
The equation of the line is y = mx + b
2y = -5x + 6
y = -5/2 x + 3
Slope, m = -5/2
y-intercept = 3
Question 4.
2x – 7y = 10
Answer:
Given,
The equation of the line is y = mx + b
2x – 7y = 10
-7y = -2x + 10
7y = 2x – 10
y = 2/7 x – 10/7
Slope, m = 2/7
y-intercept = 10/7
Use the given slope and y-intercept of a line to write an equation in slope-intercept form.
Question 5.
Slope, m =\(\frac{1}{2}\)
y-intercept, b = 3
Answer:
The equation of the line is y = mx + b
y = \(\frac{1}{2}\)x + 3
Question 6.
Slope, m = -2
y-intercept, b = 5
Answer:
The equation of the line is y = mx + b
y = -2x + 5
Solve. Show your work.
Question 7.
A line has the equation 4y = 3x – 8. Find an equation of a line parallel to this line that has a y-intercept of 2.
Answer:
A line has the equation 4y = 3x – 8.
y = 3/4 x – 2
A line parallel to this line that has a y-intercept of 2
y = 3/4 x + 2
Question 8.
A line has the equation 3y = 3 – 2x. Find an equation of a line parallel to this line that has a y-intercept of 5.
Answer:
A line has the equation 3y = 3 – 2x.
y = 1 – 2/3 x
y = -2/3 x + 1
y-intercept = 5
y = -2/3 x + 5
Question 9.
Math Journal Ira says that the graphs of the equations y = -3x + 7 and y = 3x – 7 are parallel lines. Do you agree? Explain.
Answer:
No. The slope of the equation y = -3x + 7 is -3 and the slope of the equation y = 3x – 7 is 3.
So, the graphs of the equations are not parallel lines.
Question 10.
Find an equation of the line that passes through the point (0, 4) and has a slope of –\(\frac{1}{3}\).
Answer:
Slope = –\(\frac{1}{3}\)
y-intercept = 4
The equation of the line is y = mx + b
y = –\(\frac{1}{3}\)x + 4
Question 11.
A line has slope –\(\frac{1}{2}\) and passes through the point (-4, -2). Write an equation of the line.
Answer:
The equation of the line is y = mx + b
slope = –\(\frac{1}{2}\)
y – intercept = -2
y = –\(\frac{1}{2}\)x – 2
Question 12.
Find an equation of the line that passes through the point (-5, 7) and is parallel to y = 4 – 3x.
Answer:
The equation of the line is y = mx + b
y = 4 – 3x
y = -3x + 4
y = -3x + 7
Question 13.
Find an equation of the line that passes through the point (0, 2) and is parallel to 6y = 5x – 24.
Answer:
6y = 5x – 24
The equation of the line is y = mx + b
y = 5/6 x – 4
The line that passes through the point (0, 2)
y = 5/6 x + 2
Question 14.
Find an equation of the line that passes through the pair of points (-5, -1) and (0, 4).
Answer:
The line passes through the points (-5, -1) and (0, 4).
Slope m = \(\frac{4-(-1)}{0-(-5)}\)
= \(\frac{5}{5}\)
= 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 15.
Find an equation of the line that passes through the pair of points (-3, 2) and (-2, 5).
Answer:
The line passes through the points (-3, 2) and (-2, 5)
Slope m = \(\frac{5-2}{-2-(-3)}\)
= \(\frac{3}{1}\)
= 3
The line passes through the y-axis at the point (0, 0).
Thus m = 3 and y-intercept b is 0.
y = 3x
Question 16.
Math Journal Can you write a linear equation in the slope-intercept form using the points (3, 4) and (5, 8)? Explain.
Answer:
The line passes through the points (3, 4) and (5, 8)
Slope m = \(\frac{8-4}{5-3}\)
= \(\frac{4}{2}\)
= 2
The line passes through the y-axis at the point (0, 0).
Thus m = 2 and y-intercept b is 0.
y = 2x