Question

The table below shows Katie's bank account balance at the end of the first three months of the year. If she deposits $180 in April and makes no withdrawals, find the rate of change from January to April.

A) $101/month
B) $75.75/month
C) -$19/month
D) $14.25/month
E) -$84/month

Answer 1

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.

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

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{525})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{828}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{828}-\stackrel{y1}{525}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{1}}} \implies \cfrac{ \stackrel{\$}{303} }{ \underset{months}{3} } \implies \cfrac{\stackrel{\$}{101}}{\underset{months}{1}}\implies 101~(\$)/(month)`

Answer 2

The answer is A) $101