To put the equation $3x - 3y = 15$ into slope-intercept form, we need to solve for $y$.

Step 1: Subtract $3x$ from both sides

$-3y = -3x + 15$

Step 2: Divide both sides by $-3$ to solve for $y$

$y = \frac{-3x + 15}{-3}$

Step 3: Simplify the fractions

$y = \frac{-3x}{-3} + \frac{15}{-3}$ $y = x - 5$

Thus, the equation in slope-intercept form is: $y = x - 5$

Final form:

The slope-intercept form is $y = x - 5$, where the slope $m = 1$ and the y-intercept $b = -5$.

Would you like further details or have any questions? Here are some related questions:

1. How do you determine the slope and y-intercept from a given equation?
2. What is the geometric interpretation of the slope?
3. How does changing the slope affect the graph of a line?
4. How can you find the x-intercept of a line given its equation?
5. How do you convert a slope-intercept form back into standard form?

Tip: In slope-intercept form $y = mx + b$, the coefficient $m$ represents the slope of the line and $b$ is the y-intercept.