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