Question

Consider the equations below:

y = 2x and 6x = 3y + 5

Are the lines parallel or perpendicular?

A Parallel because the product of the slopes is -1.

B Parallel because the slopes are the same.

C Perpendicular because the product of the slopes
is -1.

D Perpendicular because the slopes are the same.

Answer 1

Answer: B) Parallel because the slopes are the same

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Step-by-step explanation:

Let's solve 6x = 3y + 5 for y

6x = 3y + 5

6x-5 = 3y

3y = 6x-5

y = (6x-5)/3

y = (6x)/3 - (5/3)

y = 2x - (5/3)

This final equation is in the form y = mx+b with m = 2 as the slope and b = -5/3 as the y intercept.

With the equation y = 2x, aka y = 2x+0, the m and b values are m = 2 and b = 0 respectively.

We see that both equations have the same slope (m = 2), but different y intercepts. Therefore, the two lines are parallel. If both y intercepts were the same as well, then we'd be talking about the same identical line.

If the slopes multiplied to -1, then the lines are perpendicular. In any other case, the two lines are neither parallel nor perpendicular.