Q27. - Algebra 2

Question

Determine the value of r so that the line through $\left(6,r\right)$ and $\left(9,2\right)$ has slope $\frac{1}{3}.$

Step-by-Step Solution

Answer

The value of r is 1.

Step 1- Given information

A pair of points $\left(6,r\right),\left(9,2\right)$ and slope(m) is $\frac{1}{3}$.

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, $(x_1,y_1)=\left(6,r\right){\text{ and (x}}_2,y_2)=\left(9,2\right)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow \frac{1}{3}=\frac{2-r}{9-6}\\ \Rightarrow \frac{1}{3}=\frac{2-r}{3}\\ \Rightarrow 1=2-r\\ \Rightarrow r=1\end{array}$

Hence, the value of r is 1.