Question

Find the value of $(x+5)$, if the slope of line joining $(x,-2)$ and $(8,-11)$ is $\frac{-3}{4}$.

Answer 1

Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ $=$ $\frac{y_2-y_1}{x_2-x_1}$
Slope of the line passing through $(x,-2)$ and $(8,-11)=-\frac{3}{4}$

$\Rightarrow \frac{-11-(-2)}{8-x}=-\frac{3}{4}$.

On cross - multiplying, we get

$-3\times (8-x)=-9\times 4$

$\Rightarrow -24+3x=-36$

$\Rightarrow 3x=-12$

$\Rightarrow x=-4$

Thus the value of $x+5$ is $-4+5=1$

Thus the answer is $1$