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

Option C. -5x − 3y = 0

Explanation:

we know that

AB passes through A(-3, 0) and B(-6, 5)

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(5-0)/(-6+3)`

`m=(5)/(-3)`

`m=-(5)/(3)`

step 2

Find the slope of the line that passes through the origin and is parallel to AB

remember that

If two lines are parallel, then their slopes are the same

therefore

The slope is
`m=-(5)/(3)`

step 3

Find the equation of the line that passes through the origin and is parallel to AB

The equation in point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=-(5)/(3)`

`point(0,0)`

substitute

`y-0=-(5)/(3)(x-0)`

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

Multiply by 3 both sides to remove the fraction

`3y=-5x`

`-5x-3y=0`