Answer:
C. [tex]y-4=-\frac{9}{11}(x+8)[/tex]
Step-by-step explanation:
The point slope form is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope,
First we are going to calculate [tex]m[/tex]:
If you have two points:
[tex]A=(x_1,y_1)\\B=(x_2,y_2)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case: A=(-8,4) and B=(3,-5)
[tex]x_1=-8, y_1=4\\x_2=3, y_2=-5[/tex]
Replacing in the formula:
[tex]m=\frac{-5-4}{3-(-8)}=-\frac{9}{11}[/tex]
Then [tex]y-y_1=-\frac{9}{11}(x-x_1)[/tex],
Now we have to replace with: [tex]x_1=-8, y_1=4[/tex],
[tex]y-y_1=-\frac{9}{11}(x-x_1)\\\\y-4=-\frac{9}{11}(x-(-8))\\\\y-4=-\frac{9}{11}(x+8)[/tex]
Then the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) is:
C. [tex]y-4=-\frac{9}{11}(x+8)[/tex]
