Let's take the points (2,18) and (6,40) to find the slope (or rate of change) of the linear function:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{40-18}{6-2}=\frac{22}{4}=\frac{11}{2} \\ \Rightarrow m=\frac{11}{2} \end{gathered}[/tex]
Since the slope is m=11/2 = 5.5, then the hourly fee is $5.5
Now, we can find the maintenance fee by using the slope-intercept formula with the slope that we have and any point on the table. Let's take the point (2,18) to find the maintenance fee:
[tex]\begin{gathered} y=mx+b \\ b\colon\text{ maintenance f}e \\ (x,y)=(2,18) \\ m=\frac{11}{2} \\ \Rightarrow18=\frac{11}{2}(2)+b \\ \Rightarrow18=11+b \\ \Rightarrow b=18-11=7 \\ b=7 \end{gathered}[/tex]
we have that b = 7, this means that the maintenance fee is $7.
The equation of this function then is y = 11/2 x + 7
Finally, if we want to rent the bike for 5 hours, we have to make x=5 and solve for y:
[tex]\begin{gathered} y=\frac{11}{2}x+7 \\ x=5 \\ \Rightarrow y=\frac{11}{2}(5)+7=\frac{55}{2}+7=27.5+7=34.5 \\ y=34.5 \end{gathered}[/tex]
therefore, it costs $34.5 to rent the bike for 5 hours.
