Question

Find the slope of the line passing through the points $P(7,3)$ and $Q(0,-4)$ and find slope of line (i) parallel to PQ (ii) perpendicular to PQ.

Answer 1

Let $(x_1,y_1)=(7,3)$ and $(x_2,y_2)=(0,-4)$
Slope$=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-3}{0-7}=\frac{-7}{-7}$
Slope$=1$
$\therefore$Slope of PQ$=1$
(i) Slope of a line parallel to PQ$=1$ $[\because$ for parallel lines, $m_1=m_2]$
(ii) Slope of a line perpendicular to PQ$=-1[\because$ for perpendicular lines, $m_1\times m_2=-1]$