Chapter 1.5, Problem 20E

To determine

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

Answer to Problem 20E

Parallel

Explanation of Solution

Given information:

  $\begin{array}{l}y+4x-2=0\mathrm{...}(1)\\ y+4x+1=0\mathrm{...}(2)\end{array}$

Calculation:

The slope-intercept equation is as follows:

  $y=mx+b$

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

  $\begin{array}{l}y+4x-2=0\\ y=-4x+2\end{array}$

Compare the above equation with slope intercept equation to get,

  $\begin{array}{l}m=-4\\ b=2\end{array}$

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

  $\begin{array}{l}y+4x+1=0\\ y=-4x-1\end{array}$

Compare above equation with slope intercept equation to get,

  $\begin{array}{l}m=-4\\ b=-1\end{array}$

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