To determine the slope-intercept form of the equation, we need to rearrange it to isolate y on one side. Let's start by simplifying the equation:
9 + (27/2)x = (-3/2)y
To get rid of the fractions, we can multiply the entire equation by 2:
2 * (9 + (27/2)x) = 2 * (-3/2)y
18 + 27x = -3y
Now, let's isolate y by dividing the entire equation by -3:
(18 + 27x) / -3 = y
Simplifying further:
-6 - 9x = y
Now we have the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Comparing it to our equation, we can determine the values:
Slope (m) = -9
Y-intercept (b) = -6
Therefore, the slope of the given equation is -9, and the y-intercept is -6.