the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
Kimtoya is riding according to the equation y = 12.5x, which is in slope-intercept form where the slope is 12.5, so her rate is 12.5.
now, Sidney's rate... hmmm we don't know, but we have her table ahaa!, well, let's use that to get the slope or rate for Sydney let's pick two points from it hmmm say (2 , 25) and hmmm (5 , 62.5)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{25})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{62.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{62.5}-\stackrel{y1}{25}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}}\implies \cfrac{37.5}{3}\implies 12.5[/tex]
holy molly!, whaddaya know, they're both riding at the same rate, 12.5 km/hr
