Question

Complete the equation of the line through (3,-8)(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis and (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis.

Answer 1

`y = (4)/(3)x - 12`

Explanation:

Given

`(x_1,y_1) = (3,-8)`

`(x_2,y_2) = (6,-4)`

Required

Determine the equation

First, we need to determine the slope (m):

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (-4 - (-8))/(6 -3)`

`m = (-4 +8)/(3)`

`m = (4)/(3)`

Next, we determine the line equation using:

`y - y_1 = m(x - x_1)`

Where

`m = (4)/(3)`

`(x_1,y_1) = (3,-8)`

`y - (-8) = (4)/(3)(x - 3)`

`y +8 = (4)/(3)(x - 3)`

`y +8 = (4)/(3)x - 4`

`y = (4)/(3)x - 4 - 8`

`y = (4)/(3)x - 12`