In this phone plan, which part of the cost changes when you use more minutes, and which part stays the same no matter how many minutes you use?

Slope tells you how much the cost changes when the number of minutes increases by 1. Put that idea into a sentence about this phone plan.

In Desmos, type y = 0.75x + 25 to graph the total monthly cost as a function of minutes $x$.

Click the gear icon next to the equation (or the table icon) to create a table of values. Look at how the $y$-value changes when $x$ increases by 1 (for example, from $x = 10$ to $x = 11$). Note the consistent change in $y$ for each 1-minute increase in $x$, and interpret that change in the context of the phone plan.

The function is

This is in the form $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. So the slope of the graph is $0.75$.

Slope is the rate of change: how much the output changes when the input increases by 1.

Here:

• Input variable: $m$ (number of minutes used)
• Output variable: $C(m)$ (total monthly cost in dollars)

So the slope tells us how many dollars the cost changes when the number of minutes increases by 1 minute.

If $m$ increases by 1 minute, $C(m)$ increases by $0.75$ dollars. That means the company adds $0.75$ to the bill for each additional minute of usage.

So the correct interpretation of the slope is: The phone company charges $0.75 per minute of usage.