The slope-intercept form of the equation of a line is
y = mx + b
where m = slope, and b is the y-intercept.
Solve your equation for y.
6x + 3y = -9
3y = -6x - 9
y = -2x - 3
Now compare this equation with
y = mx + b
m = slope = -2, and b = -3
The slope is -2, and the y-intercept is -3.
