Chapter 3.3, Problem 6BGP

To determine

To Find: The value of ‘r’ so that the line passing through points $\left(r,-6\right)\&\left(5,-8\right)$ is having slope $m=-8$

Answer to Problem 6BGP

  $r=\frac{19}{4}$

Explanation of Solution

Given information:

Line passing through $\left(r,-6\right)\&\left(5,-8\right)$ and having slope $m=-8$

Concept and Formula Used:

Slope of line passing through two points is given by $m=\left(\frac{y_2-y_1}{x_2-x_1}\right)$ .

Calculation:

It is given that line passing through $\left(r,-6\right)\&\left(5,-8\right)$ .

Slope of line is given by

  $\begin{array}{l}m=\left(\frac{y_2-y_1}{x_2-x_1}\right)\\ \text{where }\left(x_1,y_1\right)=\left(r,-6\right),\left(x_2,y_2\right)=\left(5,-8\right)\&m=-8\\ -8=\left(\frac{-8-\left(-6\right)}{5-r}\right)\\ -8=\left(\frac{-8+6}{5-r}\right)\\ \text{Cross multiply}\\ -8\times \left(5-r\right)=-2\\ -40+8r=-2\left(\text{distributive property}\right)\\ \text{Add 40 on both sides}\\ -40+8r+40=-2+40\\ 8r=38\\ r=\frac{38}{8}\\ r=\frac{19}{4}\end{array}$

Conclusion:

  $r=\frac{19}{4}$