Question

Using slopes, find the value of $x$ so that the points $(6,-1),(5,0)$ and $(x,3)$ are collinear.

Answer 1

Let $A(6,-1),B(5,0)$ and $C(x,3)$

Given that $A,B$ and $C$ are collinear.

$\therefore$ Slope of line $AB=$Slope of line $BC$

$\frac{0-(-1)}{5-6}=\frac{3-0}{x-5}$

$\frac{1}{-1}=\frac{3}{x-5}$

$\Rightarrow x-5=-3$

$\Rightarrow x=5-3=2$

Hence the value of $x$ is $2$.