Chapter 1.5, Problem 13E

To determine

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

Answer to Problem 13E

Parallel

Explanation of Solution

Given information:

  $\begin{array}{l}y-7x+5=0\mathrm{...}\text{(1)}\\ y-7x-9=0\mathrm{...}\text{(2)}\end{array}$

Calculation:

The slope-intercept equation is as follows:

  $y=mx+b$

Convert equation (1) in slope intercept form as shown below.

  $\begin{array}{l}y-7x+5=0\\ y=7x-5\end{array}$

Compare the above equation with slope intercept equation to get,

  $\begin{array}{l}m=7\\ b=-5\end{array}$

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

  $\begin{array}{l}y-7x-9=0\\ y=7x+9\end{array}$

Compare above equation with slope intercept equation to get,

  $\begin{array}{l}m=7\\ b=9\end{array}$

Since, the slope of both the lines is equal to each other i.e. $\left(\parallel m=m\right)$ . So, the two lines are parallel to each other.