Question

write an equation for a line parallel to and a line perpendicular to the given line.y = -2x + 5(make up points, they are not given)

Answer 1

Parallel: y = -2x + 9

Perpendicular: y = (1/2)x + 2

Step-by-step explanation:

If we have an equation with the form y = mx + b. The value of m, the number beside the x, is the slope.

Then, 2 lines are parallel if they have the same slope. So, a parallel line to the given line is:

y = -2x + 9

On the other hand, two lines are perpendicular if the product of both slopes is equal to -1. So, the slope of the perpendicular equation is:

`\begin{gathered} -2\cdot m=-1 \\ m=(-1)/(-2) \\ m=(1)/(2) \end{gathered}`

Then, a perpendicular line to the given line is:

y = (1/2)x + 2