Question

How do you write an equation in slope-intercept form of the line through point P(-10,1) with slope -5?

Answer 1

Since we're given the slope and a point, let's start with point slope form.

The point slope form is:

`y - y_0 = m(x - x_0)` where `m` is the slope and `(x_0, y_0)` is a point through which the line passes.

In our case `m=-5` and `(x_0, y_0) = (-10, 1)`, so we can write:

`y - 1 = -5(x - (-10)) = -5(x + 10)`

Slope intercept form is:

`y = mx+c` where `m` is the slope and `c` the intercept.

To rearrange in slope intercept form, add `1` to both sides to get:

`y = -5(x+10)+1`

`= -5x-50+1`

`= -5x - 49`

This is pretty much slope intercept form with slope `m=-5` and intercept `c = -49`.

If we are really picky, we might write:

`y = -5x + -49`

Answer 2

The equation in slope-intercept form is `y=-5x-49`.

Slope-intercept form: `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

Substitute the known values into the equation, then solve for `b`.

#y=1 #m`=-5`
`x=-10`

`y=mx+b` =

`1=-5(-10)+b` =

`1=50+b`

`-49=b`

`y=-5x-49`