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