Question

What is the relationship between the lines with the following equations? 2x + 8y = 16. y = 4x + 7 The lines are parallel The lines are neither parallel nor perpendicular The lines are perpendicular The lines are the same

Answer 1

(C)The lines are perpendicular

Step-by-step explanation:

First, we make y the subject of the equation in 2x + 8y = 16.

`\begin{gathered} 2x+8y=16 \\ 8y=-2x+16 \\ y=-(2)/(8)x+(16)/(8) \\ y=-(1)/(4)x+2 \end{gathered}`

The slope of the line = -1/4

In the line y=4x+7, the slope of the line = 4

`-(1)/(4)*4=-1`

Two lines are perpendicular if the product of their slopes = -1.

Therefore, the lines are perpendicular.