Chapter 4.6, Problem 6PSA

To determine

To find: The value of $k$ .

Answer to Problem 6PSA

  $32$ .

Explanation of Solution

Given information:

Line $\overleftrightarrow{AB}$ has a slope of $2\frac{1}{2}$ .

  $A=\left(2,7\right),B=\left(12,k\right)$ .

Concept used: Slope of a line passing through two points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given as $m=\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$

Calculation:

Line $\overleftrightarrow{AB}$ has a slope of $2\frac{1}{2}$ .

  $A=\left(2,7\right),B=\left(12,k\right)$ .

  $\begin{array}{l}\text{So, 2}\frac{1}{2}=\frac{k-7}{12-2}\\ \Rightarrow \frac{5}{2}=\frac{k-7}{10}\\ \Rightarrow 2k-14=50\\ \Rightarrow 2k=64\\ \Rightarrow k=32\end{array}$

Hence, value of $k$ is $32$ .