The lines 5x + 2y = 14 and y = –5x + 9 area. parallel  b. perpendicular  c. neither

We want to see if two given lines are parallel, perpendicular, or neither.

We will see that the correct option is c, neither.

Let's see how to get that solution:

A general line in slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are parallel if they have the same slope but different y-intercept.

Two lines are perpendicular if the slope of one is equal to the opposite of the inverse slope of the other.

So we need to see if one of these two things happens.

The given lines are:

5x + 2y = 14

y = - 5x + 9

Isolating y in the first line gives:

2y = 14 - 5x

y = -(5/2)*x + 7

So in one case the slope is -5 and in the other, the slope is -5/2, so neither the lines are parallel nor perpendicular.

The correct option is c.

If you want to learn more, you can read:

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5x + 2y = 14

2y = -5x + 14

 y = -5/2 x + 7; slope m = -5/2

y = –5x + 9 ; slope m = -5.

Parallel lines slopes are equal and perpendicular slopes are opposite and reciprocal.

So both lines are neither parallel nor perpendicular

Answer

C. Neither.

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step-by-step explanation: