Question

AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to AB?

Answer 1

Answer:

C.  -5x − 3y = 0

Step-by-step explanation:

A(-3, 0) and B(-6, 5)

First we find the slope of line AB

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{5-0}{-6+3} =\frac{-5}{3}$

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 = $\frac{-5}{3}$

The line passes through the origin (0,0)

Use equation y-y1= m (x-x1)

m = -5/3 , x1=0 and y1=0

$y-0 = \frac{-5}{3}(x-0)$

$y= \frac{-5}{3}(x)$

multiply the whole equation by 3

3y = -5x

Subtract 3x from both sides

0=-5x-3y

-5x - 3y =0