#### Answer

(a) slope $=-\frac{4}{3}$
(b) Refer to the graph below.

#### Work Step by Step

Solve for $y$:
$4x+3y=12
\\4x+3y-4x=12-4x
\\3y=-4x+12
\\\frac{3y}{3}=\frac{-4x+12}{3}
\\y=\frac{-4x}{3}+\frac{12}{3}
\\y=-\frac{4}{3}x+4$
This means the given equation is equivalent to $y=-\frac{4}{3}x+4$.
RECALL:
In the linear equation $y=mx + b$, $m$=slope and $(0, b)$ is the y-intercept.
(a) The line $y=-\frac{4}{3}x+4$ has a slope of $-\frac{4}{3}$ and a y-intercept of $(0, 4)$.
(b) To graph the line, perform the following steps:
(1) Plot the y-intercept $(0, 4)$.
(2) Use the slope to plot another point.
The slope is $-\frac{4}{3}=\frac{-4}{3}$ so there is a 4-unit decrease in the value of $y$ for every 3-unit increase in $x$. From $(0, 4)$, move 5 units down (the rise) and 3 units to the right (the run) to reach $(3, 0)$. Plot $(3, 0)$.
(3) Complete the graph by connecting the two points using a line.
(Refer to the graph in the answer part above.)