When a problem says "$0.05$ dollars for each text message" and there are $t$ messages, what multiplication expression represents the total texting cost?

Should the flat fee of $15$ be multiplied by $t$, or should it be added to the texting cost? Look for an equation that adds the flat fee to the per-text charge times $t$.

In Desmos, use $x$ to represent the number of texts. Type each option as a separate function, for example: y = 15x + 0.05, y = 0.05x + 15, y = 15 + 0.05, and y = 15(0.05x).

Add a point or table for $x=0$ for each function (click the gear icon and add a table, or just look at the y-intercept). The correct equation will have a y-value of $15$ when $x=0$, because you must still pay the flat monthly fee even if you send no texts.

Choose a small number of texts, like $x=10$. Compute the expected cost by hand (flat fee plus $0.05$ times $10$), then see which function in Desmos gives that same y-value at $x=10$. Select the answer choice that matches this behavior.

The problem says there is a flat monthly fee of $15$. That means you pay $15$ no matter how many text messages you send, even if you send $0$ messages.

So the fixed part of the cost is a constant: $15$.

You are also charged $0.05$ dollars for each text message.

If you send $t$ text messages, the total texting cost is:

• cost per text $\times$ number of texts
• which is $0.05 \times t$, or $0.05t$.

This is the part of the cost that changes when $t$ changes.

The total monthly cost $C$ is the sum of the flat fee and the texting cost:

Written in the usual order (variable term first), the equation that represents the total monthly cost is $C = 0.05t + 15$.