Answer
$a)$
$y=-\dfrac{2}{3}x-2$
$b)$
$m=-\dfrac{2}{3}$ and $b=-2$
$c)$
Work Step by Step
$4x+6y+12=0$
The slope-intercept form of the equation of a line $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept
$a)$
$4x+6y+12=0$
Take $4x$ and $12$ to the right side of the equation:
$6y=-4x-12$
Take the $6$ to divide the right side:
$y=-\dfrac{2}{3}x-2$
The equation is now in slope-intercept form.
$b)$
Comparing the obtained equation to the slope-intercept form of the equation of a line shown at the top, it can be seen that $m=-\dfrac{2}{3}$ and $b=-2$
The slope of the given line is $m=-\dfrac{2}{3}$ and its $y$-intercept is $(0,-2)$
$c)$
The graph is shown below:
