Chapter 1.5, Problem 14E

To determine

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

Answer to Problem 14E

None of these

Explanation of Solution

Given information:

  $\begin{array}{l}y=\frac{1}{3}\text{x+11 }\mathrm{...}\text{(1)}\\ y=3x-9\mathrm{...}\text{(2)}\end{array}$

Calculation:

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

  $\begin{array}{l}m=\frac{1}{3}\\ b=11\end{array}$

Compare equation (2) with slope intercept equation to get,

  $\begin{array}{l}m=3\\ b=-9\end{array}$

Since, the slope of both the lines is not equal to each other i.e. $\left(\parallel m\ne m\right)$ . So, the two lines are not parallel to each other.

Since, the slope of both the lines is not opposite reciprocal of each other i.e. $\left(\perp m\ne -\frac{1}{m}\right)$ . So, the two lines are not perpendicular to each other.

Since, the slope and y- intercepts are not same for both the lines, so they are not coinciding to each other.