Answer:
Point-slope form: [tex]y-2=-\frac{1}{3} (x-6)[/tex]
Slope-intercept form: [tex]y=-\frac{1}{3}x+4[/tex]
Step-by-step explanation:
So, first, we need point-slope form.
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex]
In this form, m is your slope and [tex]x_1, y_1[/tex] is your point.
We have two points, so let's find the slope.
Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
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.
[tex]x_2[/tex] = -9
[tex]y_2[/tex] = 7
[tex]x_1[/tex] = 6
[tex]y_1[/tex] = 2
Let's put the values into the formula.
[tex]\frac{7-2}{-9-6}[/tex] = [tex]\frac{5}{-15}[/tex] = [tex]-\frac{1}{3}[/tex]
The slope is 1/3. Going back to point-slope form, let's put the slope in.
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-y_1=-\frac{1}{3} (x-x_1)[/tex]
Now, lets put our x_1, y_1 point in.
[tex]y-2=-\frac{1}{3} (x-6)[/tex]
This is our point-slope form.
Now, to convert this to slope-intercept form, multiply everything out.
[tex]y-2=-\frac{1}{3}x+2[/tex]
Add two.
[tex]y=-\frac{1}{3}x+4[/tex]
This is our slope-intercept form.
Hope this helped!
