Chapter 3.3, Problem 13CYU

To determine

The value of r so that the line passing through the points $\left(5,2\right),\text{ and }\left(-7,r\right)$ has the slope $m=\frac{5}{6}$ .

Answer to Problem 13CYU

  $r=-8$

Explanation of Solution

Given information:

The pair of points, $\left(5,2\right),\text{ and }\left(-7,r\right)$ and the slope $m=\frac{5}{6}$ .

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 $\left(5,2\right),\text{ and }\left(-7,r\right)$ is $m=\frac{5}{6}$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(5,2\right),\text{ and }\left(x_2,y_2\right)=\left(-7,r\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ \frac{5}{6}=\frac{r-2}{-7-5}\\ \frac{5}{6}=\frac{r-2}{-12}\\ 5\cdot \left(-12\right)=6\cdot \left(r-2\right)\\ -60=6r-12\\ -60+12=6r-12+12\\ -48=6r\\ \frac{-48}{6}=r\\ \Rightarrow r=-8\end{array}$

Thus, the value of r is $r=-8$ .