After writing $y = -4x + b$, plug in $x=3$ and $y=2$ from the point $(3,2)$ to create an equation you can solve for $b$.

Once you find $b$, remember that the $y$-intercept is the point where $x=0$. How can you write that point using $b$?

Type the equation in point-slope form into Desmos: $y - 2 = -4(x - 3)$. This uses the given slope $-4$ and the point $(3,2)$.

Look at where the graphed line crosses the $y$-axis (where $x=0$). Click that intersection point and note its coordinates; the $y$-intercept is that point, and its $y$-value is the $b$ in $y=mx+b$.

A convenient form for a line is the slope–intercept form:

Here, $m$ is the slope and $b$ is the $y$-intercept. You are told the slope is $-4$, so substitute $m=-4$:

Now you just need to find the value of $b$.

The line passes through $(3,2)$, which means when $x=3$, $y=2$ must satisfy the equation.

Substitute $x=3$ and $y=2$ into $y=-4x+b$:

Compute $-4(3)$ and solve for $b$:

• $-4(3) = -12$, so the equation becomes $2 = -12 + b$.
• Add $12$ to both sides: $2 + 12 = b$, so $b = 14$.

Now you know the full equation of the line: $y = -4x + 14$.

In the equation $y = mx + b$, the $y$-intercept is the point where the line crosses the $y$-axis. This happens when $x=0$, so the $y$-intercept has coordinates $(0,b)$.

You found $b=14$, so the $y$-intercept is $(0,14)$, which corresponds to answer choice C.