Once you know the cost per mile, write an equation in the form $C = (\text{cost per mile})m + b$ and use one point from the table to solve for $b$.

After you find an equation for $C$ in terms of $m$, rearrange it so that all terms are on one side and the other side is just a constant, like in the answer choices.

Create a table and in the first column (e.g., $x_1$) type the miles $6$, $9$, and $12$, and in the second column (e.g., $y_1$) type the corresponding costs $15.75$, $20.25$, and $24.75$.

Below the table, type y1 ~ a x1 + b to perform a linear regression. Desmos will display values for $a$ (the slope) and $b$ (the starting cost).

Use the $a$ and $b$ values that Desmos shows to write the equation $C = am + b$, then rearrange it into a form like the answer choices (all terms on one side, constant on the other) and select the option that matches your rearranged equation.

Because the relationship is linear, the cost per mile is constant.

Compute the change in cost when the miles increase from $6$ to $9$:

The miles increase from $6$ to $9$:

So the slope (cost per mile) is

This means the cost increases by $1.5$ dollars for each additional mile.

Write the linear equation in slope-intercept form $C = 1.5m + b$, where $b$ is the starting cost when $m = 0$.

Use any data point, for example $(m, C) = (6, 15.75)$:

Compute $1.5(6)$:

So

Thus the taxi has a fixed starting fee of $6.75$ dollars before any miles are driven.

Now substitute the slope and intercept into the equation $C = 1.5m + b$:

To compare with the choices, clear decimals by multiplying both sides by $2$:

Move all terms to one side:

This exactly matches choice D, so the correct equation is $2C - 3m = 13.5$.