Question

Determine the value of r so that a line through the points (r,3) and (5,-4) has a slope of -1/2

Answer 1

$\bf (\stackrel{x_1}{r}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-3}{5-r}=\stackrel{\stackrel{slope}{\downarrow }}{-\cfrac{1}{2}}\implies \cfrac{-7}{5-r}=\cfrac{1}{-2} \\\\\\ 14=5-r\implies 9=r$

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