Question

A line passes through the points (2,4) and (5,6) . Select Yes or No to tell whether each equation describes this line. Equation Yes No y−6=32(x+5) ​y−4=23(x−2)​ ​y−4=32(x+2)​ ​y−6=23(x−5)​

Answer 1

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-4}{5-2}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{2}{3}(x-2)$