After simplifying, you should have something of the form $f(\text{number})+7$. Look at the two points given for $f$; which point tells you the value of $f$ at that input?

Once you know $f(3)$ from the appropriate point, substitute it into $g(4)=f(3)+7$ and simplify to get the final value.

In one expression line, define the slope of $f$ using the two points: type

m = (8 - (-4))/(-1 - 3)

Desmos will display the numerical value of $m$, the slope of the line through $(3,-4)$ and $(-1,8)$.

In a new expression line, use the slope $m$ and the point $(3,-4)$ to define $f$:

f(x) = m*(x - 3) - 4

This tells Desmos the equation of the linear function $f$ that passes through the two given points.

Now define the new function in Desmos:

g(x) = f(2x - 5) + 7

Then, on a separate line, type g(4). The numerical output that Desmos shows for g(4) is the value of $g(4)$ for this problem.

Start with the definition of g:

Now plug in $x=4$ and simplify inside the function $f$ first:

So finding $g(4)$ is the same as finding $f(3)$ and then adding 7.

You are told that the linear function $f$ passes through the point $(3,-4)$.

For any function, a point $(x,y)$ on its graph means $f(x)=y$.

So from $(3,-4)$, we know directly that

There is no need to find the full equation of $f$ to get this value.

From Step 1, we have $g(4)=f(3)+7$, and from Step 2 we found $f(3)=-4$.

Substitute this into the expression for $g(4)$:

So the value of $g(4)$ is $\boxed{3}$.