Chapter 4.3, Problem 46HP

To determine

To graph: a line that is parallel and a line that is perpendicular to $y=2x-1$ ..

Answer to Problem 46HP

The line parallel to $y=2x-1$ is $y=2x+5$

The line perpendicular to $y=2x-1$ is $y=\frac{-1}{2}x+5$ .

Explanation of Solution

Given information:

Calculation:

Two lines are parallel if slope are same.

Two lines are perpendicular if slopes are negative reciprocal to each other.

Given $y=2x-1$ .

The given line has a slope $m=2$ .

SO a line parallel to $y=2x-1$ has a slope of 2.

Therefore we can say that the desired parallel line is will differ the given line by a constant number only.

  $y=2x+5$ can be a line parallel to $y=2x-1$ .

Two lines to be perpendicular to each other the slope must be negative reciprocal to each other

Given the slope is 2. Hence negative reciprocal of 2 is $\frac{-1}{2}$ and we can have any constant number.

Therefore the desired perpendicular line to $y=2x-1$ is

  $y=\frac{-1}{2}x+5$ .