To write the equation \(3y = 6x - 18\) in slope-intercept form, which is \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), we need to solve for \(y\).
Starting with the original equation:
\[ 3y = 6x - 18 \]
Divide each term by 3:
\[ y = \frac{6x}{3} - \frac{18}{3} \]
This simplifies to:
\[ y = 2x - 6 \]
So the equation in slope-intercept form is:
\[ y = 2x - 6 \]
Here, the slope \(m\) is 2 and the y-intercept \(b\) is -6.