Answer
$a)$
$y=-\dfrac{2}{3}x+6$
$b)$
$m=-\dfrac{2}{3}$ and $b=6$
$c)$
Work Step by Step
$2x+3y-18=0$
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
$a)$
$2x+3y-18=0$
Take $2x$ and $18$ to the right side of the equation:
$3y=-2x+18$
Take the $3$ to divide the right side:
$y=-\dfrac{2}{3}x+6$
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 $b=6$
The slope of the given line is $m=-\dfrac{2}{3}$ and its $y$-intercept is $(0,6)$
$c)$
The graph is shown below:
