Chapter 4.3, Problem 3GP

To determine

To find: whether the graphs of given equations are parallel or perpendicular.

Answer to Problem 3GP

Equations $6x-2y=-2$ & $y=3x-4$ are parallel to each other.

The equation $y=4$ is neither parallel nor perpendicular to $6x-2y=-2$ & $y=3x-4$ .

Explanation of Solution

Given information:

Given equations are

1. $6x-2y=-2$
2. $y=3x-4$
3. $y=4$

Calculation:

  $y=mx+b$ is the slope intercept form of the line.

Consider the first equation

  $\begin{array}{c}6x-2y=-2\\ -2y=-2-6x\\ y=3x+1\end{array}$

Therefore, slope $\left(m_1\right)=3$ .

Consider the second equation

  $y=3x-4$

Therefore slope $\left(m_2\right)=3$

Given the third equation $y=4$ .

Therefore slope $\left(m_3\right)=0$