For a linear function, the slope is the constant change in $f(x)$ divided by the change in $x$. Use two points from the table to calculate this slope.

Once you know the slope $m$, plug it into $f(x)=mx+b$ along with one point from the table (like $x=1$, $f(x)=5$) to solve for $b$.

After you have an equation, compare it to the answer choices and make sure it gives the correct $f(x)$ values for all three $x$ values in the table.

In Desmos, type each option as a separate equation: y = 2x + 3, y = 3x + 2, y = 4x + 1, and y = 5x.

Add a table (using the "+" button) with $x$-values $1$, $3$, and $5$, and a second column for $f(x)$ where you enter $5$, $13$, and $21$ to represent the given data points.

Look at which line passes through all three plotted points from the table. The function whose graph contains all three points is the one defined by the table.

For a quicker check, use Desmos’s table-of-values feature for each function (click the gear icon next to the equation and select “table”), then look at the outputs when $x=1,3,5$ and see which function produces $5$, $13$, and $21$ respectively.

For a linear function, the equation has the form

where $m$ is the slope (rate of change) and $b$ is the $y$-intercept.

Use any two points from the table, for example $(1,5)$ and $(3,13)$.

Compute the slope $m$ using

Check with another pair, say $(3,13)$ and $(5,21)$:

The slope is consistently $4$.

Now plug the slope $m=4$ and one of the points, say $(1,5)$, into $f(x)=mx+b$ to solve for $b$.

Use $x=1$ and $f(x)=5$:

So $b=1$.

Substitute $m=4$ and $b=1$ into the linear form $f(x)=mx+b$:

This matches answer choice C.