Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 4 Lesson 4.2 Understanding Slope-Intercept Form to finish your assignments.

## Math in Focus Grade 8 Course 3 A Chapter 4 Lesson 4.2 Answer Key Understanding Slope-Intercept Form

**Technology Activity**

Materials

graphing calculator

EXPLORE THE RELATIONSHIP BETWEEN y = mx AND y = mx + b

Work in pairs

Answer:

**Math Journal** The equation of another line is given by 2y = 5x – 4. It can also be written as y = 2.5x – 2. Predict the y-intercept. Use the graphing calculator to check your prediction. Is your prediction correct?

Answer:

Slope m = 2.5

y-intercept = -2

### Math in Focus Grade 8 Chapter 4 Lesson 4.2 Guided Practice Answer Key

**Write an equation for each line.**

Question 1.

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

Slope m = \(\frac{?-?}{?-?}\)

= \(\frac{?}{?}\)

=

The line intersects the y-axis at the point (, ).

So, the y-intercept is .

So, the equation of the line is .

Answer:

The line passes through the points (6, 3) and (-4, -2).

Slope m = \(\frac{6-(-4)}{3-(-2)}\)

= \(\frac{10}{5}\)

= 2

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

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

y = 2x

Question 2.

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

Slope m = \(\frac{?-?}{?-?}\)

= \(\frac{?}{?}\)

=

The line intersects the y-axis at the point (, ).

So, the y-intercept is .

So, the equation of the line is .

Answer:

The line passes through the points (1, -6) and (-4, 9).

Slope m = \(\frac{9-(-6)}{-4-1}\)

= \(\frac{15}{-5}\)

= -3

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

So, the y-intercept is -3.

So, the equation of the line is y = -3x -3.

Question 3.

Answer:

The line passes through the points (-5, -2) and (1, -2).

Slope m = \(\frac{-2-(-2)}{1+5}\)

= \(\frac{0}{6}\)

= 0

The line intersects the y-axis at the point (0, -2).

So, the y-intercept is -2.

So, the equation of the line is y = 0x -2.

Question 4.

Answer:

The line passes through the points (0, 2) and (2, 4).

Slope m = \(\frac{4-2)}{2-0}\)

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

= 1

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

So, the y-intercept is 0.

So, the equation of the line is y = -2x + 2

### Math in Focus Course 3A Practice 4.2 Answer Key

**Identify the y-Intercept. Then calculate the slope using the points indicated.**

Question 1.

Answer:

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

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

= \(\frac{5}{5}\)

= 1

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

So, the y-intercept is 0.

So, the equation of the line is y = x.

Question 2.

Answer:

The line passes through the points (0, -1) and (2, -3).

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

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

= -1

The line intersects the y-axis at the point (0, -1).

So, the y-intercept is -1.

So, the equation of the line is y = -1x -1.

Question 3.

Answer:

The line passes through the points (0, 3) and (8, -6).

Slope m = \(\frac{-6-3}{8-0}\)

= \(\frac{-9}{8}\)

m = \(\frac{-9}{8}\)

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

So, the y-intercept is 3.

Question 4.

Answer:

The line passes through the points (0, 2) and (4, 6).

Slope m = \(\frac{6-2}{4-0}\)

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

m = 1

The line intersects the y-axis at the point (0, -2).

So, the y-intercept is -2.

**Write an equation in the form y = mx or y = mx + b for each line.**

Question 5.

Answer:

The line passes through the points (4, 3) and (-4, -3).

Slope m = \(\frac{-3-3}{-4-4}\)

= \(\frac{-6}{-8}\)

= \(\frac{3}{4}\)

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

So, the y-intercept is 0.

So, the equation of the line is y = \(\frac{3}{4}\)x

Question 6.

Answer:

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

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

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

= \(\frac{-3}{2}\)

The line intersects the y-axis at the point (0, 1).

So, the y-intercept is 1.

So, the equation of the line is y = \(\frac{-3}{2}\)x +1.

Question 7.

Answer:

The line passes through the points (-8, 3) and (0, -2).

Slope m = \(\frac{-2-3}{0+8}\)

= \(\frac{-5}{8}\)

The line intersects the y-axis at the point (0, -2).

So, the y-intercept is -2.

So, the equation of the line is y = \(\frac{-5}{8}\)x -2.

Question 8.

Answer:

The line passes through the points (0, 4) and (-3, -2).

Slope m = \(\frac{-2-4}{-3-0}\)

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

= 2

The line intersects the y-axis at the point (0, 4).

So, the y-intercept is 4.

So, the equation of the line is y = 2x + 4

**Graph each line using 1 grid square to represent 1 unit on both axes for the interval from -4 to 4. Then write the equation for each line.**

Question 9.

The line passes through the points (-4, 3) and (-4, -2).

Answer:

Question 10.

The line passes through the points (-3, 4) and (1, 4).

Answer:

Question 11.

**Math Journal** Line A passes through the origin and has a negative slope. Line B has a positive y-intercept and a positive slope. Line C has a negative slope and a negative y-intercept. Give a possible equation for each line. Justify your answer.

Answer:

Possible equations: Line A: y = -3x; Line B: y = 5x + 2; Line C: y = -2x – 7.

For line A, the value of m in the equation y = mx + b is negative and the value of b is 0.

For line B, both m and b have positive values. For line C, both m and b have negative values.