Chapter 3, Problem 22MCQ

To determine

To Find: The value of ‘r’ so that the line passing through points $\left(-4,8\right)\&\left(r,12\right)$ is having slope $m=\frac{4}{3}$

Answer to Problem 22MCQ

  $r=-1$

Explanation of Solution

Given information:

Line passing through $\left(-4,8\right)\&\left(r,12\right)$

Concept and Formula Used:

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

Calculation:

It is given that line passing through $\left(-4,8\right)\&\left(r,12\right)$ .

Slope of line is given by

  $\begin{array}{l}m=\left(\frac{y_2-y_1}{x_2-x_1}\right)\\ \text{where }\left(x_1,y_1\right)=\left(-4,8\right),\left(x_2,y_2\right)=\left(r,12\right)\&m=\frac{4}{3}\\ \frac{4}{3}=\left(\frac{12-\left(8\right)}{r-\left(-4\right)}\right)\\ \frac{4}{3}=\frac{4}{r+4}\\ 4\left(r+4\right)=4\times 3\\ 4r+16=12\\ 4r=12-16\\ 4r=-4\\ r=-1\end{array}$

Conclusion:

  $r=-1$