Question

The graph above shows the

high temperatures of a city
on certain days in July. Find
the rate of change from the
12th to the 24th
A) -0.5%/day
B) 0.5%/day
C) -2°/day
D) 2°/day
E) 2.5°/day

Answer 1

The correct answer is D

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.

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

`(\stackrel{x_1}{12}~,~\stackrel{y_1}{90})\qquad (\stackrel{x_2}{24}~,~\stackrel{y_2}{96}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{96}-\stackrel{y1}{90}}}{\underset{\textit{\large run}} {\underset{x_2}{24}-\underset{x_1}{12}}} \implies \cfrac{ 6 }{ 12 } \implies \cfrac{\stackrel{degree}{1} }{ \underset{day}{2} }\implies 0.5~(degree)/(day)`