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.

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Solution

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 $= 1$
$∴$ Slope of PQ $= 1$
(i) Slope of a line parallel to PQ $= 1$ $[∵$ for parallel lines, $m_{1} = m_{2}]$
(ii) Slope of a line perpendicular to PQ $= - 1 [∵$ for perpendicular lines, $m_{1} \times m_{2} = - 1]$

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