Question:
Find the value of x so that the line through (3, x) and (2, 7) is parallel to the line through (-1, 4) and (0, 6).
Solution:
We know that for two lines to be parallel, their slope must be the same. The given points are A(3,x),B(2,7) and C(-1,4),D(0,6)
slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$
$\Rightarrow\left(\frac{6-4}{0+1}\right)=\left(\frac{7-x}{2-3}\right)$
$\Rightarrow\left(\frac{2}{1}\right)=\left(\frac{7-x}{-1}\right) \Rightarrow-2=7-x$
⇒x = 9
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