Use the two points to calculate the slope with the formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$. Is the slope positive or negative?

Once you know the slope $m$, plug it into $f(x) = mx + b$ and use one of the points to solve for $b$.

After you have an equation, plug in $x=3$ and $x=5$ to see if you get $7$ and $11$. Eliminate any choices that do not give both values.

In Desmos, add a table and enter the two points $(3,7)$ and $(5,11)$ so you can see where the graph of the correct function must pass.

Type each choice as an equation in Desmos: $y = 2x + 1$, $y = 2x - 1$, $y = x/2 + 1$, and $y = -2x + 1$. You will see four straight lines.

Look at which line passes exactly through both plotted points $(3,7)$ and $(5,11)$. The equation of that line matches the correct answer choice.

A linear function $f$ with $f(3)=7$ and $f(5)=11$ can be thought of as a line passing through the points $(3,7)$ and $(5,11)$ in the coordinate plane.

Use the slope formula for a line through $(x_1,y_1)$ and $(x_2,y_2)$:

Here $(x_1,y_1) = (3,7)$ and $(x_2,y_2) = (5,11)$, so

So the slope of the linear function is $2$.

A linear function can be written as $f(x) = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

We already found $m = 2$, so write

Now use one of the given points, for example $(3,7)$, which means when $x=3$, $f(x)=7$:

Now substitute $b=1$ into the equation $f(x)=2x+b$ to get the function:

Compare this with the answer choices and select the one that exactly matches this equation.