Answer
a) See graph
b) $-\dfrac{3}{4}$
Work Step by Step
a) We are given the line:
$3x+4y=12$
Determine the intercepts:
$x=0\Rightarrow 3(0)+4y=12\Rightarrow y=3$
$y=0\Rightarrow 3x+4(0)=12\Rightarrow x=4$
Plot the points $(0,3)$ and $(4,0)$ and join them with a line:
b) Rewrite the equation of the line in the form $y=mx+b$:
$3x+4y=12$
$4y=-3x+12$
$y=-\dfrac{3}{4}x+3$
The slope of the line is:
$m=-\dfrac{3}{4}$
Any line parallel to this line has the same slope:
$m=-\dfrac{3}{4}$
