Question

Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.

(-9,7), (6,2)​

Answer 1

Point-slope form:
`y-2=-(1)/(3) (x-6)`

Slope-intercept form:
`y=-(1)/(3)x+4`

Explanation:

So, first, we need point-slope form.

Point-slope form:
`y-y_1=m(x-x_1)`

In this form, m is your slope and
`x_1, y_1` is your point.

We have two points, so let's find the slope.

Slope formula:
`(y_2-y_1)/(x_2-x_1)`

The y_2 and y_1 points can be interchanged, but order can't be changed (a y_2 can't go with an x_2).

For this problem, (-9,7) is going to be the x_2, y_2 pair.

`x_2` = -9

`y_2` = 7

`x_1` = 6

`y_1` = 2

Let's put the values into the formula.

`(7-2)/(-9-6)` =
`(5)/(-15)` =
`-(1)/(3)`

The slope is 1/3. Going back to point-slope form, let's put the slope in.

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

`y-y_1=-(1)/(3) (x-x_1)`

Now, lets put our x_1, y_1 point in.

`y-2=-(1)/(3) (x-6)`

This is our point-slope form.

Now, to convert this to slope-intercept form, multiply everything out.

`y-2=-(1)/(3)x+2`

Add two.

`y=-(1)/(3)x+4`

This is our slope-intercept form.

Hope this helped!