Q28. - Algebra 2

Question

Determine the value of r so that the line through $\left(5,r\right)$ and $\left(2,3\right)$ has slope $2.$ 

Step-by-Step Solution

Answer

The value of r is $9$.

Step 1- Given information

A pair of points $\left(5,r\right),\left(2,3\right)$ and slope(m) is $2$.

Step 2- Formula used

The slope formula of a line is:

 $m=\frac{y_2-y_1}{x_2-x_1}$

Where, $m$ is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{ and }{x}_1\ne x_2.$

Step 3- To find the slope

Here, $(x_1,y_1)=\left(5,r\right){\text{ and (x}}_2,y_2)=\left(2,3\right)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow 2=\frac{3-r}{2-5}\\ \Rightarrow 2=\frac{3-r}{-3}\\ \Rightarrow -6=3-r\\ \Rightarrow r=3+6\\ \Rightarrow r=9\end{array}$

Hence, the value of r is $9$.