Question

The value of $x$, such that the line through $(3,x)$ and $(2,7)$ is parallel to the line through $(-2,3)$ and $(0,5)$, is

Answer 1

Let $m_1$ be the slope of line passing through $(3,x)$ and $(2,7)$
$m_1=\frac{7-x}{2-3}$
and $m_2$ be the slope of line passing through $(-2,3)$ and $(0,5)$
$m_2=\frac{5-3}{0-(-2)}=\frac{2}{2}=1$
As lines are parallel,
so, $m_1=m_2$
$\Rightarrow \frac{7-x}{2-3}=1\Rightarrow x=8$