Question

a lines in the xy-plane passes through the point (4,1) and has a slope of (-1/4). the point (6,y) also lies on the lines. what is the value of y?

Answer 1

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-1}{6-4}=\stackrel{\textit{slope}}{-\cfrac{1}{4}}\implies \cfrac{y-1}{2}=-\cfrac{1}{4} \\\\\\ 4y-4=-2\implies 4y=2\implies y=\cfrac{2}{4}\implies y=\cfrac{1}{2}$