Chapter 1.5, Problem 18E

To determine

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

Answer to Problem 18E

None of these

Explanation of Solution

Given information:

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

Calculation:

The slope-intercept equation is as follows:

  $y=mx+b$

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

  $\begin{array}{l}m=3\\ b=-2\end{array}$

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

  $\begin{array}{l}3x+y=2\\ y=-3x+2\end{array}$

Compare above equation with slope intercept equation to get,

  $\begin{array}{l}m=-3\\ b=2\end{array}$

Since, the slope of both the lines is not equal 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-intercept of both the lines is not equal. So, the two lines are not coinciding to each other.