Question

If the points $(-3,6),(-9,a)$ and $(0,15)$ are collinear, then the value of $a$ is

Answer 1

Let the given points be $A(-3,6)$, $B(-9,a)$ and $C(0,15)$.

Since the points A, B and C are collinear, the slope of $\overleftrightarrow{AB}$ = the slope of $\overleftrightarrow{BC}$

$\Rightarrow \frac{6-a}{6}=\frac{15-a}{9}$

$\Rightarrow 18-3a=30-2a$

$\Rightarrow a=-12.$'