Answer
a) $y=-3x+12$
b) $3x+y-12=0$
Work Step by Step
a) The equation of a line in slope-intercept form is:
$$y=mx+b,$$
where $m$ is the slope and $b$ in the $y$-intercept.
We are given:
$$\begin{align*}
P(4,0)&\text{ belongs to the line}\\
Q(0,12)&\text{ belongs to the line}.
\end{align*}$$
We calculate the slope $m$ using the coordinates of the two points $P$ and $Q$:
$$\begin{align*}
m&=\dfrac{y_Q-y_P}{x_Q-x_P}\\
&=\dfrac{12-0}{0-4}\\
&=-3.
\end{align*}$$
We substitute $m=-3$ and $b=12$ in Eq. $(1)$ to determine the equation of the line:
$$y=-3x+12.\tag2$$
b) The equation of a line in general form is:
$$Ax+By+C=0.$$
Rewrite the equation $y=-3x+12$ in general form:
$$\begin{align*}
3x+y-12&=0.
\end{align*}$$
c) Graph the line using the points $P$ and $Q$:
