Chapter 1.5, Problem 8CFU

To determine

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

Answer to Problem 8CFU

Coinciding

Explanation of Solution

Given information:

  $\begin{array}{l}y=2x-8\mathrm{...}\text{(1)}\\ 4x-2y-16=0\mathrm{...}\text{(2)}\end{array}$

Calculation:

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

  $\begin{array}{l}m=2\\ b=-8\end{array}$

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

  $\begin{array}{c}4x-2y-16=0\\ -2y=-4x+16\\ y=\frac{-4}{-2}x+\frac{16}{-2}\\ y=2x-8\end{array}$

Compare the above equation with slope intercept equation to get,

  $\begin{array}{l}m=2\\ b=-8\end{array}$

Since, the slope and y-intercept of both lines is equal to each other i.e. $\left(\parallel m=m\right)\text{ and }\left(b=b\right)$ . So, the two lines are coinciding to each other.