Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?

Question

1. A. same line
2.  B. perpendicular
3.  C. neither perpendicular nor parallel
4.  D. parallel

Answer 1

Choice E: The lines are in a long-distance relationship.

Answer 2

4x - 8y = 9

8x - 7y = 9

In order to be the same line, the equations have to be multiples of each other.

4x - 8y = 9

8x - 16y = 18

See how the 2nd is twice the first? These two will produce the same line when graphed. If you can't see that, solve each for y.

4x - 8y = 9

-8y = -4x + 9

y = (1/2)x - 9/8

8x - 7y = 9

-7y = -8x + 9

y = (8/7)x - 9/7

To be the same line, the equations would be the same. Parallel lines have the same slope but different y-intercepts. Perpendicular lines have opposite, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

Your answer is C.

Answer 3

Since 4x - 8y = 9, -8y = -4x + 9. So, y = (1/2)x -9/8.

Since 8x - 7y = 9, -7y = -8x + 9. So, y = (8/7)x - 9/7

The slopes of the lines are 1/2 and 8/7, respectively.

So, since parallel lines have the same slope and since the slopes of perpendicular lines are negative reciprocals of each other, the lines are neither parallel nor perpendicular.