The $y$-intercept is the point where the graph crosses the $y$-axis. How does that tell you the value of $b$ in $y=mx+b$?

Once you know $b$, use the point $(4,2)$ and substitute $x=4$ and $y=2$ into $y=mx+b$ to make an equation you can solve for $m$.

After you find $m$ and $b$, write the equation $f(x)=mx+b$ and then see which answer choice matches it exactly.

In Desmos, enter each equation on its own line: y=(3/4)x+5, y=-(3/4)x+5, y=(3/2)x+5, and y=-(3/2)x+5. Each will appear as a different line on the graph.

Look at where each line crosses the $y$-axis. All four should cross at $(0,5)$, since they all have $+5$ as the constant term. This confirms the $y$-intercept condition is met for each.

Click on the graph near $x=4$ and use the point-tracing feature, or type the point (4,2) as a separate expression. See which line goes exactly through $(4,2)$. The equation of that line is the correct choice.

A linear function in slope-intercept form looks like $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.

The problem says the graph has a $y$-intercept of 5. That means when $x=0$, $y=5$, so $b=5$.

So the function must look like

for some slope $m$.

We are told that the graph passes through the point $(4,2)$. That means when $x=4$, the output is $f(4)=2$.

Use this in the equation $f(x)=mx+5$:

Now solve this equation for $m$.

Solve the equation from the last step:

So the slope is $m=-\tfrac{3}{4}$.

Substitute $m=-\tfrac{3}{4}$ and $b=5$ into $f(x)=mx+5$:

This matches answer choice B, so the correct equation is $f(x)=-\tfrac{3}{4}x+5$.