## Engage NY Eureka Math 8th Grade Module 4 Lesson 20 Answer Key

### Eureka Math Grade 8 Module 4 Lesson 20 Exercise Answer Key

Opening Exercise
Figure 1

The equation for the line in Figure 1 is y = $$\frac{2}{3}$$ x – 3.

Figure 2

The equation for the line in Figure 2 is y = – $$\frac{1}{4}$$ x + 2.

Exercises

Exercise 1.
Write the equation that represents the line shown.

y = 3x + 2

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = 3x + 2
– 3x + y = 3x – 3x + 2
– 3x + y = 2
– 1( – 3x + y = 2)
3x – y = – 2

Exercise 2.
Write the equation that represents the line shown.

y = – $$\frac{2}{3}$$ x – 1

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and 𝒂 is not negative.
y = – $$\frac{2}{3}$$ x – 1
(y = – $$\frac{2}{3}$$ x – 1)3
3y = – 2x – 3
2x + 3y = – 2x + 2x – 3
2x + 3y = – 3

Exercise 3.
Write the equation that represents the line shown.

y = – $$\frac{1}{5}$$ x – 4

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – $$\frac{1}{5}$$ x – 4
(y = – $$\frac{1}{5}$$ x – 4) 5
5y = – x – 20
x + 5y = – x + x – 20
x + 5y = – 20
x + 5

Exercise 4.
Write the equation that represents the line shown.

y = x

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = x
– x + y = x – x
– x + y = 0
– 1( – x + y = 0)
x – y = 0

Exercise 5.
Write the equation that represents the line shown.

y = $$\frac{1}{4}$$ x + 5

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = $$\frac{1}{4}$$ x + 5
(y = $$\frac{1}{4}$$ x + 5)4
4y = x + 20
– x + 4y = x – x + 20
– x + 4y = 20
– 1( – x + 4y = 20)
x – 4y = – 20

Exercise 6.
Write the equation that represents the line shown.

y = – $$\frac{8}{5}$$ x – 7

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – $$\frac{8}{5}$$ x – 7
(y = – $$\frac{8}{5}$$ x – 7)5
5y = – 8x – 35
8x + 5y = – 8x + 8x – 35
8x + 5y = – 35

### Eureka Math Grade 8 Module 4 Lesson 20 Problem Set Answer Key

Question 1.
Write the equation that represents the line shown.

y = – $$\frac{2}{3}$$ x – 4

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – $$\frac{2}{3}$$ x – 4
(y = – $$\frac{2}{3}$$ x – 4)3
3y = – 2x – 12
2x + 3y = – 2x + 2x – 12
2x + 3y = – 12

Question 2.
Write the equation that represents the line shown.

y = 8x + 1

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = 8x + 1
– 8x + y = 8x – 8x + 1
– 8x + y = 1
– 1( – 8x + y = 1)
8x – y = – 1

Question 3.
Write the equation that represents the line shown.

y = $$\frac{1}{2}$$ x – 4

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = $$\frac{1}{2}$$ x – 4
(y = $$\frac{1}{2}$$ x – 4)2
2y = x – 8
– x + 2y = x – x – 8
– x + 2y = – 8
– 1( – x + 2y = – 8)
x – 2y = 8

Question 4.
Write the equation that represents the line shown.

y = – 9x – 8

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – 9x – 8
9x + y = – 9x + 9x – 8
9x + y = – 8

Question 5.
Write the equation that represents the line shown.

y = 2x – 14

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = 2x – 14
– 2x + y = 2x – 2x – 14
– 2x + y = – 14
– 1( – 2x + y = – 14)
2x – y = 14

Question 6.
Write the equation that represents the line shown.

y = – 5x + 45

Use the properties of equality to change the equation from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – 5x + 45
5x + y = – 5x + 5x + 45
5x + y = 45

### Eureka Math Grade 8 Module 4 Lesson 20 Exit Ticket Answer Key

Question 1.
Write an equation in slope – intercept form that represents the line shown.

y = – $$\frac{1}{3}$$ x + 1

Question 2.
Use the properties of equality to change the equation you wrote for Problem 1 from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = – $$\frac{1}{3}$$ x + 1
(y = – $$\frac{1}{3}$$ x + 1)3
3y = – x + 3
x + 3y = – x + x + 3
x + 3y = 3

Question 3.
Write an equation in slope – intercept form that represents the line shown.

y = $$\frac{3}{2}$$ x + 2

Question 4.
Use the properties of equality to change the equation you wrote for Problem 3 from slope – intercept form, y = mx + b, to standard form, ax + by = c, where a, b, and c are integers, and a is not negative.
y = $$\frac{3}{2}$$ x + 2
(y = $$\frac{3}{2}$$ x + 2)2