#### Answer

slope=-$\frac{3}{4}$

#### Work Step by Step

When an equation is written in slope-intercept form, or y=mx+b form, m=slope and b=y-intercept. To determine the slope of the line defined by the equation 3x+4y=-8, we'll rewrite the equation in y=mx+b form by solving for y, then observing what the slope is. To do this, our first step will be to isolate the 4y term be subtracting 3x on both sides of the equation, to get
4y=-8-3x
Then, to solve for y, we'll divide by 4 on both sides of the equation to get
$\frac{4y}{4}$=$\frac{-8-3x}{4}$
y=$\frac{-8}{4}$-$\frac{3x}{4}$
y=-2-$\frac{3}{4}$x
y=-$\frac{3}{4}$x-2 (Rearrange)
Now that the equation is in y=mx+b form, we can easily see that the slope of the line=-$\frac{3}{4}$