How do you find the slope-intercept form for 3y+2x+12=0?

3y + 2x + 12 = 0.

y = mx + b,
Solve the given Eq for y:
3y = -2x - 12,
Divide both sides by 3:
y = (-2/3)x - 4.

To find the slope-intercept form of a linear equation, we need to rearrange the given equation into the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

Given equation: 3y + 2x + 12 = 0

Step 1: Move the term with the variable y to the isolated side.
Subtract 2x from both sides:
3y = -2x - 12

Step 2: Divide both sides of the equation by the coefficient of y (which is 3) to isolate y.
Divide both sides by 3:
y = (-2/3)x - 4

Now, the equation is in slope-intercept form, y = mx + b, where m = -2/3 is the slope and b = -4 is the y-intercept.

Therefore, the slope-intercept form for the equation 3y + 2x + 12 = 0 is y = (-2/3)x - 4.