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

parallel means "same slope (m)"

m = $\frac{y2 - y1}{x2 - x1}$ = $\frac{0 - 5}{-3 - (-6)} = \frac{-5}{-3 + 6} = \frac{-5}{3}$

Now, input the point (0, 0) and the slope $(\frac{-5}{3})$ into the Point-Slope formula:

y - y₁ = m(x - x₁)

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

    y = $\frac{-5}{3}x$

 3y = -5x    multiplied both sides by 3

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

Answer: C