Question

Line 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 Line AB? A. 5x − 3y = 0 B. -x + 3y = 0 C. -5x − 3y = 0 D. 3x + 5y = 0 E. -3x + 5y = 0

Answer 1

0 = -5x - 3y subtracted 3y from both sides

Explanation:

Answer 2

parallel means "same slope (m)"

m =
`(y2 - y1)/(x2 - x1)` =
`(0 - 5)/(-3 - (-6)) = (-5)/(-3 + 6) = (-5)/(3)`

Now, input the point (0, 0) and the slope
`((-5)/(3))` into the Point-Slope formula:

y - y₁ = m(x - x₁)

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

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

3y = -5x multiplied both sides by 3

0 = -5x - 3y subtracted 3y from both sides

Answer: C