To rewrite the equation $13x - 3y = -12$ in slope-intercept form, we need to solve for $y$. The slope-intercept form of a line is:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

1. Start with the given equation: $13x - 3y = -12$

2. Subtract $13x$ from both sides: $-3y = -13x - 12$

3. Divide every term by $-3$ to solve for $y$: $y = \frac{13}{3}x + 4$

Thus, the equation in slope-intercept form is: $y = \frac{13}{3}x + 4$

Would you like more details on this solution or have any questions?

Here are 5 related questions:

1. What is the slope of the line $13x - 3y = -12$?
2. How do you determine the y-intercept from an equation?
3. How would you graph $y = \frac{13}{3}x + 4$?
4. Can you convert the slope-intercept form back to standard form?
5. How do you find the x-intercept from the equation?

Tip: In slope-intercept form, the coefficient of $x$ represents the slope of the line, and the constant term is the y-intercept.