Chapter 11.2, Problem 41STP

To determine

To calculate: The effect on the graph of the equation $y=\frac{1}{2}x$ when the equation is changed to $y=-2x$ .

Answer to Problem 41STP

(I) The graph is rotated $90°$ about the origin.

Explanation of Solution

Given information: Equation $y=\frac{1}{2}x$ and $y=-2x$

Formula used: Slope of equation $y=mx$ where m is constant is m.

Graph:

  

Calculation: Slope of $y=\frac{1}{2}x$ is $\frac{1}{2}$ .

Slope of $y=-2x$ is-2.

Product of slopes is -1.

So, equations $y=\frac{1}{2}x$ and $y=-2x$ are perpendicular to each other.

Thus, (I) The graph is rotated $90°$ about the origin when the equation $y=\frac{1}{2}x$ is changed to $y=-2x$ .