Answer:
C. -5x − 3y = 0
Step-by-step explanation:
A(-3, 0) and B(-6, 5)
First we find the slope of line AB
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{5-0}{-6+3} =\frac{-5}{3}[/tex]
Slope of the line parallel to AB = slope of line AB
When the lines are parallel then their slope are equal
So the slope of line parallel to AB = [tex]\frac{-5}{3}[/tex]
The line passes through the origin (0,0)
Use equation y-y1= m (x-x1)
m = -5/3 , x1=0 and y1=0
[tex]y-0 = \frac{-5}{3}(x-0)[/tex]
[tex]y= \frac{-5}{3}(x)[/tex]
multiply the whole equation by 3
3y = -5x
Subtract 3x from both sides
0=-5x-3y
-5x - 3y =0
