Question

Why are the lines y = 5x − 1 and 10x + 2y = 0 perpendicular

Answer 1

The line are not perpendicular. Perpendicular lines after opposite reciprocals.

Explanation:

Change 10x + 2y = 0 into the slope intercept form of a line.

Subtract 10x from both sides

10x - 10x + 2y = 0 - 10 x

2y = -10x Divide both sides by 2

y = -10x/2

y = -5x.

The slope of the first equation is 5 ( y = 5x -1 ).

The slope of the second equation is -5 ( y = -5x )

The opposite reciprocal of 5 would be -1/5 not -5.

So these lines are not perpendicular.

Helping in the name of Jesus.

Answer 2

The lines are not perpendicular because the product of their slopes is not -1.

Explanation:

y = 5x - 1

slope = 5

10x + 2y = 0

2y = -10x

y = -5x

slope = -5

The slopes are 5 and -5.

5 × (-5) = -25

The product of the slopes is -25, not -1, so the lines are not peropendicular.