In a linear model like $y = mx + b$, $b$ is the value of $y$ when $x = 0$. In $C = 3.50 + 2.25m$, what is the value of $C$ when $m = 0$?

If you got into the taxi and then got out without traveling any miles, what cost would the equation give you? What kind of fee does that sound like?

In Desmos, enter the equation C = 3.5 + 2.25m. If Desmos prefers x and y, you can instead type y = 3.5 + 2.25x.

Either look at the graph’s $y$-intercept (the point where it crosses the vertical axis) or create a table and check the value of $C$ (or $y$) when $m$ (or $x$) is $0$. The constant value you see there is what the $3.50$ represents in the real-world situation.

The cost model is $C = 3.50 + 2.25m$.

• $C$ is the total cost of the ride, in dollars.
• $m$ is the number of miles.
• $2.25$ is multiplied by $m$, so that term changes as the miles change.
• $3.50$ is a constant term that does not depend on $m$.

In a linear equation of the form $y = mx + b$, the constant $b$ is the value of $y$ when $x = 0$ (the starting value). Here, $3.50$ plays that role.

To understand the constant term, set the number of miles to zero.

If $m = 0$ (no miles traveled), then

So $C = 3.50 + 0 = 3.50$.

This tells you the total cost of the ride even when the taxi does not move any miles.

From Step 2, when $m = 0$ miles, the total cost $C$ is $3.50$. That means $3.50$ is the fixed amount you pay at the start, before any distance is traveled. Among the choices, this corresponds to “The initial fee, in dollars, before any miles are traveled.”