[tex]\bf \begin{array}{|cc|ll} \cline{1-2} \stackrel{Time}{hours}&\stackrel{distance}{miles}b\\ \cline{1-2} 2&90\\ \underline{3}&\underline{135}\\ 5&225\\ \underline{6}&\underline{270}\\ \cline{1-2} \end{array}~\hspace{7em} (\stackrel{x_1}{3}~,~\stackrel{y_1}{135})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{270})[/tex]
[tex]\bf \stackrel{\stackrel{\textit{constant of}}{\textit{proportionality}}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{270-135}{6-3}\implies \cfrac{135}{3}\implies \stackrel{\textit{unit rate}}{\cfrac{45~miles}{1~hour}}\implies 45 \\\\\\ \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-135=45(x-3) \\\\\\ y-135=45x-135\implies y=45x[/tex]
of course, if we use "t" and "d" instead, we can also write it as d = 45t.
