Assume $f(x)=mx+b$. Substitute into $g(x)=2f(-x)+5$ and simplify to identify the slope and intercept of $g$ in terms of $m$ and $b$.

Find the slope and y-intercept of $g$ from the two intercepts on the graph, then set them equal to the slope and intercept you got from simplifying $2f(-x)+5$.

From the graph, use the intercepts as points: $(-3,0)$ and $(0,\frac{11}{2})$.

In Desmos, plot the two points (-3,0) and (0,11/2).

Then type y=mx+b and adjust sliders so the line passes through both points, or compute directly from the two points. You should get slope $\frac{11}{6}$ and intercept $\frac{11}{2}$ for $g(x)$.

Let $f(x)=mx+b$. Using $g(x)=2f(-x)+5$, rewrite as $g(x)=(-2m)x+(2b+5)$.

Match slope and intercept with $g(x)$ to solve for $m$ and $b$, then write $f(x)=mx+b$.

Let the graphed function be $g(x)=2f(-x)+5$.

From the graph, $g$ crosses the x-axis at $(-3,0)$ and the y-axis at $(0,\frac{11}{2})$.

So the slope of $g$ is

and the y-intercept is $g(0)=\frac{11}{2}$.

Because $f$ is linear, write $f(x)=mx+b$.

Then

So the slope of $g$ is $-2m$, and the y-intercept of $g$ is $2b+5$.

Match coefficients with the slope and intercept from the graph.

Slope:

Intercept:

Substitute $m=-\frac{11}{12}$ and $b=\frac{1}{4}$ into $f(x)=mx+b$: