Question

What is the equation of the line shown in the graph in slope-point form?

Answer 1

The point-slope form is `y+6=1/5(x-4)` or `y+5=1/5(x-9)`, depending on which point you use. If you solve for `y` to get the slope-intercept form, both equations will convert to `y=1/5x-34/5`.

Explanation:

We have to find the slope first.

I found two points on the line that we can use to find the slope:

`(4,-6)` and `(9,-5)`

Use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`,

where:

`m` is the slope, and `(x_1,y_1)` is one point, and `(x_2,y_2)` is the other point. I'm going to use `(4,-6)` for `(x_1,y_1)`, and `(9,-5)` for `(x_2,y_2)`.

`m=(-5-(-6))/(9-4)`

`m=1/5`

We could have determined the slope by starting at `(4,-6)` and counting how many spaces to move up and over to get to `(9,-5)`, which would give you `1/5`.

Now that we have the slope, we can determine the point-slope form for this line.

The formula for the point-slope form is:

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

`m=1/5`

I'm going to use `(4,-6)` as the point.

`y-(-6)=1/5(x-4)`

`y+6=1/5(x-4)`

We can also use the second point `(9,-5)`.

`y-(-5)=1/5(x-9)`

`y+5=1/5(x-9)`

If you solve for `y`, which will convert the equation to slope-intercept form, and both equations will come out to `y=1/5x-34/5`.