Chapter 4.3, Problem 6CYU

To determine

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

Answer to Problem 6CYU

The lines $y=\frac{1}{2}x$ and $y=-\frac{1}{2}x$ are perpendicular to each other.

The lines $y=\frac{1}{2}x$ and $y=-\frac{1}{2}x$ are neither perpendicular nor parallel to $3y=x$ .

Explanation of Solution

Given information:

Given equations are

1. $y=\frac{1}{2}x$
2. $3y=x$
3. $y=-\frac{1}{2}x$

Calculation:

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

Considerthe first equation

  $y=\frac{1}{2}x$

Therefore, slope $\left(m_1\right)=\frac{1}{2}$ .

Consider the second equation

  $\begin{array}{c}3y=x\\ y=\frac{x}{3}\end{array}$

Therefore slope $\left(m_2\right)=\frac{1}{3}$

Consider the third equation

  $y=-\frac{1}{2}x$ .

Therefore slope $\left(m_3\right)=-\frac{1}{2}$

Since, $m_1{m}_3=-1$

Therefore, the lines $y=\frac{1}{2}x$ and $y=-\frac{1}{2}x$ are perpendicular to each other.

The lines $y=\frac{1}{2}x$ and $y=-\frac{1}{2}x$ are neither perpendicular nor parallel to $3y=x$ .