Answer
Slope: $-\frac{3}{4}$
$y$-intercept: $3$
Work Step by Step
The slope-intercept form of a linear equation of a non vertical line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.
We use this definition to find the slope and $y$-intercept of $3x+4y=12$
First, we must write this equation in slope intercept form.
To do so, we subtract $3x$ from each side of the equation: $4y=12-3x$
Then, we divide by $4$ on both sides of the equation: $y=-\frac{3}{4}x+\frac{12}{4}$
We simplify: $y=-\frac{3}{4}x+3$
Since $-\frac{3}{4}$ takes the place of $m$, it is the slope.
Since $3$ takes the place of $b$, it is the $y$-intercept.
