Question

Find the slope of each line.

Answer 1

to get the slope of a line all we need is two points off of it, so let's get two points from that table

`\bf ~\hspace{4em}\downarrow ~\hspace{1.5em}\downarrow \\ \begin{array} \cline{1-5} x&0&1&2&3\\ \cline{1-5} y&-(1)/(3)&(1)/(3)&1&(5)/(3) \\ \cline{1-5} \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{(1)/(3)})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{(5)/(3)})`

`\bf \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{(5)/(3)}-\stackrel{y1}{(1)/(3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{~~(4)/(3)~~}{2}\implies \cfrac{~~(4)/(3)~~}{(2)/(1)}\implies \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\cdot \cfrac{1}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{2}{3}`