Question

where y is the distance in miles and x is the time in hours. Which car is traveling at the greater​ speed?

Answer 1

the vehicle with a larger slope is the one travelling faster, since in this case the slope stands for mph, so let's check which one has the larger slope.

Car1

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{128})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{256}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{256}-\stackrel{y1}{128}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ \stackrel{ mi }{128} }{ \underset{ hours }{2} } \implies 64~(miles)/(hour)`

Car2

`y=\stackrel{\stackrel{m}{\downarrow }}{55}x\qquad \impliedby \qquad \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \qquad 55~(miles)/(hour)`

so, Car1 is clearly moving faster.