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?

A. 

5x − 3y = 0

B. 

-x + 3y = 0

C. 

-5x − 3y = 0

D. 

3x + 5y = 0

E. 

-3x + 5y = 0

Answer 1

C. -5x − 3y = 0

Explanation:

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

First we find the slope of line AB

`slope = (y_2-y_1)/(x_2-x_1) =(5-0)/(-6+3) =(-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 =
`(-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 = (-5)/(3)(x-0)`

`y= (-5)/(3)(x)`

multiply the whole equation by 3

3y = -5x

Subtract 3x from both sides

0=-5x-3y

-5x - 3y =0