Answer
x-intercept: 6
y-intercept: 4
slope = $-\frac{2}{3}$
Work Step by Step
RECALL:
x-intercept can be found by setting y=0
y=intercept can be found by setting x =0
x-intercept
Set $y=0$ to have:
$2x+3(0) -12 = 0
\\2x-12=0
\\2x=12
\\x=6$
Thus, the x-intercept is 6.
y-intercept
Set $x=0$ to have:
$2(0) +3y-12=0
\\3y-12=0
\\3y=12
\\y=4$
Thus, the y-intercept is 4.
RECALL:
The slope-intercept form of the equation of a line is $y=mx+b$ where m=slope and b=y-intercept.
Write the given equation in slope-intercept form by isolating $y$ to have:
$2x+3y-12=0
\\3y=-2x+12
\\y=\frac{-2x+12}{3}
\\y=-\frac{2}{3}x + 4$
Thus, the line has a slope of $-\frac{2}{3}$.
