Question

What is the equation of a line with `m=-5` and goes through `(8,-2)`?

Answer 1

`y = -5x + 38`

Explanation:

The general equation of a line is

`y = mx + b`
where:
`m` = slope
`b` = y-intercept

[Given]
`m = -5`
passes through `(8, -2)`

Since we know the slope, we know that our equation will follow the form:

`y = -5x + b`

Since we know that the line passes through the point `(8, -2)`, we can substitute these values to our equation above to find `b` or our y-intercept.

[Solution]
`y = -5x + b`
`-2 = -5(8) + b`
`-2 = -40 + b`
`b = 38`

So the final equation is:
`y = -5x + 38`