Question

Find the value of $y$ if the line passing through the points $(3,y)$ and $(2,7)$ is parallel to the line passing through the points $(-1,4)$ and $(0,6)$.

• A. 9
• B. -9
• C. 6
• D. -6

Answer 1

The correct option is A

9

Equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $y_2-y_1=m(x_2-x_1)$, where $m$ is the slope of the line.
We know that, the slope of the parallel lines are equal. Hence, we must have
$m_1=m_2$, where $m_1$ is the slope of the line passing through $(3,y)$ and $(2,7)$ and $m_2$ is the slope of the line passing through $(-1,4)$ and $(0,6)$.
$\Rightarrow \frac{7-y}{2-3}=\frac{6-4}{0+1}\Rightarrow \frac{7-y}{-1}=\frac{2}{1}$
$\Rightarrow y=9$