Question

What is the slope intercept form of the line passing through `(2,-3)` with a slope of `3/2`?

Answer 1

`y=3/2x+13/2`

Explanation:

Given:

Point: `(2,-3)`

Slope: `3/2`

You can use the point-slope form: `y-y_0=m(x-x_0)`, where `m` is the slope and `(x_0,y_0)` is a point on the line.

Solution:

`[1]" "y-y_0=m(x-x_0)`

Substitute the point `(2,-3)` into `(x_0,y_0)`.

`[2]" "y-2=m(x+3)`

Substitute the slope `3/2` into `m`.

`[3]" "y-2=3/2(x+3)`

Isolate `y` so you can express the line in the slope-intercept form: `y=mx+b`

`[4]" "y=3/2(x+3)+2`

Multiply `3/2` to `(x+3)`.

`[5]" "y=3/2x+9/2+2`

`[6]" "y=3/2x+9/2+4/2`

`[7]" "color(blue)(y=3/2x+13/2)`