Answer
$-7$
Work Step by Step
Substituting the point $(a,-3)$ into the given equation, $
(y-1)=\dfrac{2}{3}(x+1)
,$ and then solving for $a$ result to
\begin{align*}
(-3-1)&=\dfrac{2}{3}(a+1)
\\\\
-4&=\dfrac{2}{3}(a+1)
\\\\
3(-4)&=\left(\dfrac{2}{3}(a+1)\right)3
\\\\
3(-4)&=2(a+1)
\\\\
-12&=2a+2
\\\\
-12-2&=2a
\\\\
-14&=2a
\\\\
-\dfrac{14}{2}&=\dfrac{2a}{2}
\\\\
-7&=a
.\end{align*}
Hence, the value of $a$ is $
-7
$
