Parallel and Perpendicular Lines

Question

Which equation is parallel to -3 + 4x = y + 2x and has a y-intercept of 9?

A -2x – 3 = y

B 7x - 3 = y

C 2y – 18 = 4x

D x = y - 3

Answer 1

Because this is a multiple choice there is a quick way to solve.

Parallel lines have the same slope. If y = mx + b, then m is the slope.

Your equation is -3 + 4x = y + 2x is the same as y = 2x - 3. So your slope is 2.

This means A, B and D cannot be parallel

For good measure let's make sure C works

2y - 18 = 4x

2y = 4x + 18

y = 2x + 9

Since the b in y = mx + b is the amount raised from the origin, then it's y-intercept is 9

Answer 2

Re-arranging the given equation y = 4x - 2x -3

= 2x - 3 Comparing with y = mx + C, we know our slope (m) =2. By inspecting each of the 4 answer options for which one gives us m =2 and intercept (C) = 9, gives Option C as the correct answer because it can be re-arranged from: 2y = 4x + 18. Divide thru by 2, yields: y = 2x + 9 with our desired slope (2) and intercept (9).