Question

Use the given information to write the equation of the line in slope-intercept form: y = mx + b

through the points(−2,−1)and(3,9)

A
y=2x+3

B
y=8x−15

C
y=−2x+15

D
y=12x−3

Answer 1

`y =2x + 3`

Explanation:

Given

(-2,-1) and (3,9).

Required

Determine the line equation

First, we calculate slope (m)

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

Where

`(x_1,y_1) = (-2,-1)`

`(x_2,y_2) = (3,9)`

So, we have:

`m = (9 - (-1))/(3- (-2))`

`m = (9+1)/(3+2)`

`m = (10)/(5)`

`m = 2`

The equation is then calculated using:

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

`y - (-1) =2(x - (-2))`

`y - (-1) =2(x +2)`

`y +1 =2(x +2)`

Open bracket

`y +1 =2x + 4`

Subtract 1 from both sides

`y +1-1 =2x + 4-1`

`y =2x + 3`