Question

How do you graph the line through point (-3,-1) and slope m=-1/5?

Answer 1

`y=-1/5x+8/5`

Explanation:

We use the point-slope formula: `y-y_1=m(x-x_1)`

We know:
`m=-1/5`
A point: `(-3,-1) -> (x_1,y_1)`

Thus, we substitute all these values into the point-slope formula:

`y-(-1)=-1/5(x-(-3)) -> y+1=-1/5(x+3)`

This gives us the equation of the line with the slope `-1/5` that passes through the point `(-3,-1)` but if you need to write the equation in `y=mx+b` then here's how we do it.

So we are simply solving for `y`

`y+1=-1/5(x+3)`

`y+1=-1/5x-3/5`

`y=-1/5x-3/5-1 -> y=-1/5x(-3/5-5/5)`

`y=-1/5x+8/5`

We can verify this graphically: graph{-1/5x-8/5 [-10, 10, -5, 5]}