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Which pair of lines are perpendicular? A) y = 4x - 9 and y + 4x = 3 B) y = 3x + 7 and y + 2 = 3(x - 5) C) y = 2x and 2y = x -9 D) y + x = 0 and y = x

User Joniel
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First, take into account that the general form of a linear equation is:

y = mx + b

where m is the slope and b the y-intercept.

When two lines are parallel, their slopes are equal.

When two lines are perpendicular, you can verify the following relation between slopes:

m1 = -1/m2

Then:

A)

y = 4x - 9

y + 4x = 3 which is the same as

y = -4x + 3

In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.

Hence, the lines are not neither parallel nor perpendicular.

B)

y = 3x + 7

y + 2 = 3(x-5) which is the same as

y = 3x - 15 - 2

y = 3x - 17

In this case the slopes are the same, then, the lines are parallel

C)

y = 2x

2y = x - 9 which is the same as

y = 1/2 x - 9/2

In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.

Hence, the lines are not neither parallel nor perpendicular.

D)

y + x = 0 which is the same as

y = -x

y = x

In this case you can verify that m1 = -1/m2, then, the line are perpendicular.

User Lutzh
by
8.3k points

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