Chapter 4.3, Problem 45HP

To determine

The key features of the graph of two parallel lines and two perpendicular lineson same axes.

Explanation of Solution

The two lines in the graph beneath are equal lines: they will never meet. Notice that they have the very same steepness which implies their slopes are indistinguishable. The main distinction between the two lines is the y-catch. In the event that one line is moved vertically toward the y-intercept of the other, they turned turn into a similar line.

  

Parallel line.

  $\begin{array}{l}\begin{array}{l}f(x)=-2x+6\\ f(x)=-2x-4\end{array}\}\text{parallel}\\ \begin{array}{l}f(x)=3x+2\\ f(x)=2x+2\end{array}\}\text{nonparallel}\end{array}$

This can be decided from their conditions whether two lines are equal by looking at their inclines. On the off chance that the slants are the equivalent and the y-blocks are extraordinary, the lines are equal. In the event that the slants are unique, the lines are not equal.

In contrast to resemble lines, opposite lines do meet. Their crossing point frames a privilege or 90-degree edge. The two lines underneath are opposite.

  

Perpendicular line