Chapter 3.3, Problem 38PPS

To determine

The value of r so that the line passing through the points $\left(3,5\right),\text{ and }\left(-3,r\right)$ has the slope $m=\frac{3}{4}$ .

Answer to Problem 38PPS

  $r=\frac{1}{2}$

Explanation of Solution

Given information:

The pair of points, $\left(3,5\right),\text{ and }\left(-3,r\right)$ and the slope $m=\frac{3}{4}$ .

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

In order to find the value of r, such that the slope of the line passing through the points $\left(3,5\right),\text{ and }\left(-3,r\right)$ is $m=\frac{3}{4}$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(3,5\right),\text{ and }\left(x_2,y_2\right)=\left(-3,r\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ \frac{3}{4}=\frac{r-5}{-3-3}\\ \frac{3}{4}=\frac{r-5}{-6}\\ 3\left(-6\right)=4\left(r-5\right)\\ -18=4r-20\\ -18+20=4r-20+20\\ 2=4r\\ \frac{2}{4}=r\\ \Rightarrow r=\frac{1}{2}\end{array}$

Thus, the value of r is $r=\frac{1}{2}$ .