Question

The graph shows a line and two similar triangles. What is the equation of the line?

Answer 1

well, let's first off use two points, hmmm those ones already there, say the origin (0,0) and (6,10), so then

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{10}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-0}{6-0}\implies \cfrac{5}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{5}{3}(x-0)\implies y=\cfrac{5}{3}x \\\hspace{34em}$

Answer 2

Answer: The answer is D