Chapter 13.2, Problem 27PSC

(a)

To determine

To find: The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the x-axis.

Answer to Problem 27PSC

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over x-axis is $y=-\frac{3}{4}x+1$ .

Explanation of Solution

Given:

The equation is $y=\frac{3}{4}x-1$ .

Calculation:

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the x-axis is as follows.

  $\begin{array}{c}y=-\left(\frac{3}{4}x-1\right)\\ =-\frac{3}{4}x+1\end{array}$

Therefore, the equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over x-axis is $y=-\frac{3}{4}x+1$ .

(b)

To determine

To find: The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the y-axis.

Answer to Problem 27PSC

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over y-axis is $y=-\frac{3}{4}x-1$ .

Explanation of Solution

Given:

The equation is $y=\frac{3}{4}x-1$ .

Calculation:

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over y-axis is as follows.

  $\begin{array}{c}y=\left(\frac{3}{4}\left(-x\right)-1\right)\\ =-\frac{3}{4}x-1\end{array}$

Therefore, the equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over y-axis is $y=-\frac{3}{4}x-1$ .

(c)

To determine

To find: The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the line $y=x$ .

Answer to Problem 27PSC

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ on y-axis is $y=-\frac{3}{4}x-1$ .

Explanation of Solution

Given:

The equation is $y=\frac{3}{4}x-1$ .

Calculation:

The equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the line $y=x$ is as follows.

  $\begin{array}{c}x=\frac{3}{4}y-1\\ \frac{4}{3}x=y-\frac{4}{3}\\ y=\frac{4}{3}x+\frac{4}{3}\end{array}$

Therefore, the equation of the reflection of the graph of $y=\frac{3}{4}x-1$ over the line $y=x$ is $y=\frac{4}{3}x+\frac{4}{3}$ .