y=mx+b(m is the slope and b is y intercept.)

2x + 3y + 6 = 0

This is done by subtracting 2x from both sides

2x - 2x + 3y + 6 = 0-2x

on the left side 2x-2x cancel out and on the right side 0-2x leaves -2x so we get this

3y + 6 = -2x

next move 6 following the same procedure

3y + 6 - 6 = -2x - 6

3y = -2x - 6

finally isolate y by dividing by 3 across the equation

Now that we have convert the equation to slope intercept form we can identify the slope, which is:

-2/3