Question

Write an equation of each line that passes through the following points in slope-intercept form:

1. A (8, –1) and B (–4, 17)
2. C (–19, 31) and D (1, –9)

Answer 1

1. y = -3/2 x +11

2. y = -2 x -7

Explanation:

Slope intercept form is y = mx+b

1. A (8, –1) and B (–4, 17)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (17--1)/(-4-8)

=(17+1)/(-4-8)

=18/-12

Dividing top and bottom by 6

=-3/2

Given the slope

y = -3/2 x+b

Using the point (8,1) we can find b

-1 = -3/2(8) +b

-1 =-12 +b

Add 12 to each side

-1+12 = -12+12 +b

11 =b

The equation is y = -3/2 x +11

2. C (–19, 31) and D (1, –9)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (-9-31)/(1--19)

=(-40)/(1+19)

= -40/20

=-2

Given the slope

y = -2 x+b

Using the point (1,-9) we can find b

-9 = -2(1) +b

-9 =-2 +b

Add 2 to each side

-9+2 = -2+2 +b

-7 =b

The equation is y = -2 x -7