Question

What is the equation of the line with slope `m= -5` that passes through `(-1,-3)`?

Answer 1

`y =-5x-8`

Explanation:

Since we are provided the slope and a point on the line we can use the equation for point slope form of the equation of a line.

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

Where `m=` slope and the point is `(x_1,y_1)`

For this situation `m=-5` and a point of `(-1,-3)`

`m=-5`
`x_1=-1`
`y_1=-3`

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

Plug in the values
`y-(-3) =-5(x-(-1))`

Simplify the signs
`y+3 =-5(x+1)`

Use distributive property to eliminate the parenthesis
`y+3 =-5x-5`

Use the additive inverse to isolate the `y` value
`y cancel(+3) cancel(-3) =-5x-5-3`

Simplify the common terms
`y =-5x-8`