Find the value of $x$ if the line passing through $(x, - 3)$ and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

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Solution

Slope of line joining (7, -1) and (0, 3),
$m = \frac{3 + 1}{0 - 7} = - \frac{4}{7}$ $[1 m a r k]$
Slope of line joining (x, -3) and (-5, 1)
$= \frac{1 + 3}{- 5 - x} = \frac{4}{- 5 - x}$ $[1 m a r k]$
slope of parallel lines are equal
$\Rightarrow - \frac{4}{7} = \frac{4}{- 5 - x} \Rightarrow \frac{4}{7} = \frac{4}{5 + x} \Rightarrow 20 + 4 x = 28 \Rightarrow 4 x = 8 \Rightarrow x = 2$ $[1 m a r k]$

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Find the value of x if the line passing through (x,−3) and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

Slope of line joining (7, -1) and (0, 3), m=3+10−7=−47 [1 mark] Slope of line joining (x, -3) and (-5, 1) =1+3−5−x=4−5−x [1 mark] slope of parallel lines are equal ⇒ −47=4−5−x⇒ 47=45+x⇒ 20+4x=28⇒ 4x=8⇒ x=2 [1 mark]

Find the value of $x$ if the line passing through $(x, - 3)$ and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).