#### Answer

$6$;
$4$;
$y=-\dfrac{2}{3}x+4$;
$m=-\dfrac{2}{3}$

#### Work Step by Step

RECALL:
(1) The slope-intercept form of a line's equation is $y=mx + b$ where m = slope and b = y-intercept.
(2) The x-intercept is a point where the graph touches or crosses the x-axis.
The x-intercept can be found by setting $y=0$ then solving for $x$.
(3) The y-intercept is a point where the graph touches or crosses the y-axis.
The y-intercept can be found by setting $x=0$ then solving for $y$.
Convert $2x+3y-12=0$ to slope-intercept form by solving for $y$ to obtain:
$2x + 3y -12 -2x+12=0-2x+12
\\3y=-2x+12
\\\dfrac{3y}{3} = \dfrac{-2x+12}{3}
\\y = \dfrac{-2x}{3} + \dfrac{12}{3}
\\y = -\dfrac{2}{3}x + 4$
The equation above has a slope of $,=-\dfrac{2}{3}$ and a y-intercept of $4$.
To find the x-intercept, set $y=0$ then solve for $x$ to obtain:
$y=-\dfrac{2}{3}x+4
\\0 = -\dfrac{2}{3}x + 4
\\0+\dfrac{2}{3}x = -\dfrac{2}{3}x+4 + \dfrac{2}{3}x
\\\dfrac{2}{3}x = 4$
Multiply $\dfrac{3}{2}$ to both sides of the equation to obtain:
$\\\dfrac{3}{2} \cdot \dfrac{2}{3}x = 4 \cdot \dfrac{3}{2}
\\x = 6$
The x-intercept is $6$.