part A)
[tex]\bf \begin{array}{ccllll}
hours(x)&velocity(y)\\
-----&-----\\
1&6\\
3&2
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 6}})\quad
% (c,d)
&({{ 3}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-6}{3-1}\implies \cfrac{-4}{2}\implies -2[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-1)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-6=-2x+2\implies y=-2x+2+6\implies \boxed{y=-2x+8}[/tex]
part B)
well, we know y = -2x+8.... so.. what's the runner's velocity after 5hours? well, x = 5, thus y = -2(5) +8 ---> y = -2
to graph it, well, is a LINEar equation, meaning the graph is a LINE, and to graph a line, all you need is two points, and by now, you have more than two.. so graph it away.
