Chapter 4.3, Problem 46HP

To determine

Graph: Sketch the line that is parallel and perpendicular to line $y=2x-1$ .

Explanation of Solution

Given information: The given line is $y=2x-1$

Graph: The line parallel to line $y=2x-1$ will have same slope $m=2$ . Therefore, any line of the form $y=2x+k$ having slope $m=2$ will be parallel to line $y=2x-1$ , where $\left(k\right)$ is any constant. So, consider a line $y=2x+2$ for $\left(k=2\right)$ is a line parallel to line $y=2x-1$ . Similarly, any line perpendicular to line $y=2x-1$ will have slope $\left(m\text{'}=-\frac{1}{2}\right)$ . Therefore, the line of the form $y=-\frac{1}{2}x+k$ will be perpendicular to line $y=2x-1$ for any $k\in R$ . Hence, the line of the form $y=-\frac{1}{2}x+1$ will be perpendicular to line $y=2x-1$ .

Now, the graph for the parallel and perpendicular line to $y=2x-1$ is shown as.