Chapter 9.3, Problem 29PPS

To determine

To rotate: The line by given degree and find the equation of the resulting image.

Answer to Problem 29PPS

The equation of image about the x intercept is $y=2x+4$ and about the y intercept is $y=2x+4$ .

Explanation of Solution

Consider the line.

  $y=2x+4$

The x intercept of the line is,

  $\begin{array}{c}0=2x+4\\ x=\frac{-4}{2}\\ =-2\end{array}$

Rotate the given line about the point $\left(-2,0\right)$ through $180°$ .

The image will be parallel to the line with same x intercept.

Thus, the equation of line is,

  $y=2x+4$

The y intercept of the line is,

  $\begin{array}{c}y=2\left(0\right)+4\\ y=4\end{array}$

Rotate the given line about the point $\left(0,4\right)$ through $180°$ .

The image will be parallel to the line with same y intercept.

Thus, the equation of line is,

  $y=2x+4$

Therefore, the equation of image about the x intercept is $y=2x+4$ and about the y intercept is $y=2x+4$ .