Question

What is the equation in point-slope form and slope intercept form for the line given (9, 1) and (4, 16)?

Answer 1

The point-slope form is `y-1=-3(x-9)`, and the slope-intercept form is `y=-3x+28`.

Determine the slope, `m`, using the two points.

Point 1: `(9,1)`
Point 2: `(4,16)`

`m=(y_2-y_1)/(x_2-x_1)=(16-1)/(4-9)=(15)/(-5)=-3`

Point-slope form.

General equation: `y-y_1=m(x-x_1)`, where `x_1` and `y_1` are one point on the line. I will use Point 1: `(9,1)`.

`y-1=-3(x-9)`

Slope-intercept form.

General equation: `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

Solve the point-slope equation for `y`.

`y-1=-3(x-9)`

Distribute the `-3`.

`y-1=-3x+27`

Add `1` to each side.

`y=-3x+28`