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Rewrite the following equation in slope-intercept form.

13x − 3y = –12

Write your answer using integers, proper fractions, and improper fractions in simplest form.

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.

Rewrite the following equation in slope-intercept form: 13x − 3y = –12. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Learn how to rewrite the linear equation 13x - 3y = -12 in slope-intercept form (y = mx + b). This problem involves solving for y, identifying the slope and y-intercept, and understanding the structure of linear equations. Suitable for students in Grades 8-10.

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