Chapter 1.5, Problem 12E

To determine

To find: whether graphs of given equations are parallel, coinciding, perpendicular, or none of these.

Answer to Problem 12E

Perpendicular

Explanation of Solution

Given information:

  $\begin{array}{l}y=5x-18\mathrm{...}\text{(1)}\\ 2x+10y+10=0\mathrm{...}\text{(2)}\end{array}$

Calculation:

The slope-intercept equation is as follows:

  $y=mx+b$

Compare equation (1) with slope intercept equation to get,

  $\begin{array}{l}m=5\\ b=-18\end{array}$

Convert equation (2) in slope intercept form as shown below.

  $\begin{array}{l}2x+10y+10=0\\ 10y=-2x-10\\ y=\frac{-2x}{10}-\frac{10}{10}\\ y=\frac{-1}{5}x-1\end{array}$

Compare above equation with slope intercept equation to get,

  $\begin{array}{l}m=-\frac{1}{5}\\ b=-1\end{array}$

Since, the slope of both the lines is opposite reciprocal of each other i.e. $\left(\perp m=-\frac{1}{m}\right)$ . So, the two lines are perpendicular to each other.