Question

What is the equation of the line with slope `m= -9/5` that passes through `(-10,23)`?

Answer 1

Point-slope form: `y-23=-9/5(x+10)`

Slope-intercept form: `y=-9/5+5`

Explanation:

Point-Slope Form
When you have the slope and one point on a line, you can use the point-slope form to find the equation for the line. The general equation is `y-y_1=m(x-x_1)`, where `m=-9/5` and `(x_1,y_1)` is `(-10,23)`.

Substitute the given values into the point-slope equation.

`y-23=-9/5(x-(-10)`

Simplify.

`y-23=-9/5(x+10)`

Converting to Slope-Intercept Form
If desired, you can convert from point-slope form to slope-intercept form by solving for `y`. The general form is `y=mx+b`, where `m` is the slope, and `b` is the y-intercept.

`y-23=-9/5(x+10)`

Add `23` to both sides.

`y=-9/5(x+10)+23`

Distribute `-9/5`.

`y=-9/5x-90/5+23`

Simplify `-90/5` to `-18`.

`y=-9/5x-18+23`

Simplify.

`y=-9/5+5`, where `m=-9/5` and `b=5`.

graph{y=-9/5x+5 [-10.08, 9.92, -2.84, 7.16]}