Chapter 8.7, Problem 39HP

To determine

To describe what happens to the graph of $y=3x+4$ when the slope is changed to $\frac{1}{3}$ .

Answer to Problem 39HP

Changing the slope of the line changes the steepness of the line

Explanation of Solution

Given information: The slope of graph of $y=3x+4$ is changed to $\frac{1}{3}$

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $y=3x+4$

Solutions of the equations are calculated as follows:

When $x=0$

  $\begin{array}{l}y=3\left(0\right)+4\\ y=0+4\\ y=4\end{array}$

When $x=1$

  $\begin{array}{l}y=3\left(1\right)+4\\ y=3+4\\ y=7\end{array}$

Now, slope of the line is changed to $m=\frac{1}{3}$

Thus, the equation becomes:

  $y=\frac{1}{3}x+4$

Solutions of the equations are calculated as follows:

When $x=0$

  $\begin{array}{l}y=\frac{1}{3}\left(0\right)+4\\ y=0+4\\ y=4\end{array}$

When $x=3$

  $\begin{array}{l}y=\frac{1}{3}\left(3\right)+4\\ y=1+4\\ y=5\end{array}$

On plotting both the lines on the same graph,

  

Thus, changing the slope of the line changes the steepness of the line but it still passes through the same quadrants.

Conclusion:

Hence, changing the slope of the line changes the steepness of the line