You know $f$ is measured in dollars and $m$ is measured in miles. What kind of quantity would turn miles into dollars when multiplied by $m$?

If the number of miles increases by 1, which number in the equation tells you how much the fare changes? How would you describe that change in words?

In Desmos, type y = 2.5x + 4. Here, think of $x$ as the number of miles and $y$ as the fare in dollars.

Click the gear icon next to the equation and select "Table" (or use the + button and choose "Table"). Look at the $y$-values for $x = 1, 2, 3$, etc., and notice how much $y$ increases when $x$ increases by 1 mile.

Find the difference in the fare values when the miles go up by 1 each time (for example, from $x = 1$ to $x = 2$). Describe in words what that consistent difference tells you about how the fare depends on the number of miles.

The given equation is

Compare this to the common linear form $y = mx + b$.

• The number multiplied by the variable ($m$ here) is the slope or rate of change.
• The constant term (the number added or subtracted at the end) is the starting value or initial amount.

So in this equation, $2.5$ is the coefficient of $m$, and $4$ is the constant term.

We are told:

• $f$ is the fare in dollars.
• $m$ is the distance in miles.

Since $2.5$ is multiplied by $m$ (miles) to produce $f$ (dollars), the number $2.5$ must convert miles into dollars. That means its units are dollars per mile.

For any linear equation like $f = 2.5m + 4$:

• The coefficient of the variable ($2.5$ in front of $m$) tells how much the output ($f$) changes when the input ($m$) increases by 1 unit.

In words, this coefficient describes how the fare changes when the ride distance increases by 1 mile.

Putting it all together:

• $2.5$ has units of dollars per mile.
• It is the rate of change of the fare with respect to miles.
• So, for each additional mile traveled, the fare goes up by about $2.50.

This matches choice B) The taxi fare increases by about $2.50 for each mile traveled.