To write the linear 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 can follow these steps:
- Divide every term in the equation by 3 to solve for \(y\):
\[ y = \frac{6x}{3} - \frac{18}{3} \]
- Simplifying the equation gives:
\[ y = 2x - 6 \]
Thus, the slope-intercept form of the equation is:
\[ y = 2x - 6 \]
So, the answer is:
\[ y = 2x - 6 \]