Question

The graph shows the relationship between time

and the number of soda bottles a machine can
make. Use the points (4,64) and (6,96) to find the
number of soda bottles the machine can make
each minute.

Answer 1

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Answer 2

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.

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{64})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{96}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{96}-\stackrel{y1}{64}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{4}}}\implies \cfrac{\stackrel{bottles}{32}}{\underset{mins}{2}}\implies \cfrac{\stackrel{bottles}{16}}{\underset{mins}{1}}`