Question

Find another point on the line that passes through the point (4,5) and has a slope of 2. Explain how you obtained your answer.

Answer 1

well, we know its slope and we also know a point on it, so hmmm without further ado, we can get its equation, once we have the equation, we can get any point we like on it pretty much, so

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{2}(x-\stackrel{x_1}{4}) \\\\\\ y-5=2x-8\implies y=2x-3$

well then hmmm to get some other point hmmm let's pick a random "x" hmmm say  dunno x = -13, so

$\underline{x=-13}\hspace{5em}y=2(\stackrel{x}{-13})-3\implies y=-26-3\implies \underline{y=-29} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \underset{another~point}{(-13~~,~~-29)}~\hfill$