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Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles traveled. Is the rate of change [tex]$2.25$[/tex]?

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{Amount Juno Owed for a Taxi} \\
\hline Miles & Amount Owed (dollars) \\
\hline 1 & 2.5 \\
\hline 2 & 4.75 \\
\hline 3 & 7 \\
\hline 4 & 9.25 \\
\hline 5 & 11.5 \\
\hline
\end{tabular}

A. Yes, because the amount owed changes by [tex]$2.25$[/tex] every time the miles change by [tex]$1$[/tex].

B. No, because the amount owed does not change by [tex]$2.25$[/tex] every time the miles change by [tex]$1$[/tex].



Answer :

GinnyAnswer
To determine if the rate of change is 2.25, we will look at the increments in the amount owed for each additional mile traveled and see if this increment is consistent throughout the given data.

1. Calculate the rate of change between each consecutive mile:

- For mile 1 to mile 2:
[tex]\[ \text{Rate of change} = \frac{\text{Amount for 2 miles} - \text{Amount for 1 mile}}{2 - 1} = \frac{4.75 - 2.5}{1} = 2.25 \][/tex]

- For mile 2 to mile 3:
[tex]\[ \text{Rate of change} = \frac{\text{Amount for 3 miles} - \text{Amount for 2 miles}}{3 - 2} = \frac{7 - 4.75}{1} = 2.25 \][/tex]

- For mile 3 to mile 4:
[tex]\[ \text{Rate of change} = \frac{\text{Amount for 4 miles} - \text{Amount for 3 miles}}{4 - 3} = \frac{9.25 - 7}{1} = 2.25 \][/tex]

- For mile 4 to mile 5:
[tex]\[ \text{Rate of change} = \frac{\text{Amount for 5 miles} - \text{Amount for 4 miles}}{5 - 4} = \frac{11.5 - 9.25}{1} = 2.25 \][/tex]

2. Consistency check:
As we can see, the rate of change for each increment of one mile is indeed consistent and equals 2.25.

Therefore, the correct answer is:

Yes, because the amount owed changes by 2.25 every time the miles change by 1.

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