Question

I’ve tried many times to answer the question but my teacher keeps saying it’s wrong so can you help me please

Answer 1

Let's take the points (2,18) and (6,40) to find the slope (or rate of change) of the linear function:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(40-18)/(6-2)=(22)/(4)=(11)/(2) \\ \Rightarrow m=(11)/(2) \end{gathered}`

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:

`\begin{gathered} y=mx+b \\ b\colon\text{ maintenance f}e \\ (x,y)=(2,18) \\ m=(11)/(2) \\ \Rightarrow18=(11)/(2)(2)+b \\ \Rightarrow18=11+b \\ \Rightarrow b=18-11=7 \\ b=7 \end{gathered}`

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:

`\begin{gathered} y=(11)/(2)x+7 \\ x=5 \\ \Rightarrow y=(11)/(2)(5)+7=(55)/(2)+7=27.5+7=34.5 \\ y=34.5 \end{gathered}`

therefore, it costs $34.5 to rent the bike for 5 hours.