Question

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

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C 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 $(3,p)$ and $(2,7)$ and $m_2$ is the slope of the line passing through $(-1,4)$ and $(0,6)$.
$\Rightarrow \frac{7-p}{2-3}=\frac{6-4}{0+1}\Rightarrow \frac{7-p}{-1}=\frac{2}{1}$
$\Rightarrow 7-p=-2$
$\Rightarrow p=7+2$
$\Rightarrow p=9$