Question

If the slope of the line passing through the points (k, $-$3) and (4, 5) is $\frac{1}{2}$. Then find the value of k.

Answer 1

We know that slope of line = $\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$
Slope of the line joining the points (k, $-$3) and (4, 5) = $\frac{-3-5}{k-4}=-\frac{8}{k-4}$
It is given that slope =$\frac{1}{2}$.
$$\begin{gathered} \therefore \frac{1}{2}=-\frac{8}{k-4} \\ \Rightarrow k-4=-16 \\ \Rightarrow k=-16+4 \\ \Rightarrow k=-12 \end{gathered}$$