Chapter 1.5, Problem 7CFU

To determine

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

Answer to Problem 7CFU

Parallel

Explanation of Solution

Given information:

  $\begin{array}{l}y=x-6\mathrm{...}\text{(1)}\\ x-y+8=0\mathrm{...}\text{(2)}\end{array}$

Calculation:

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

  $\begin{array}{l}m=1\\ b=-6\end{array}$

Convert equation (2) into slope intercept equation to get,

  $\begin{array}{l}x-y+8=0\\ y=x+8\end{array}$

Compare the above equation with slope intercept equation to get,

  $\begin{array}{l}m=1\\ b=8\end{array}$

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.