write the equation 3x-2y=-12 in slope intercept form

To convert the equation \( 3x - 2y = -12 \) into slope-intercept form (\( y = mx + b \)), follow these steps:

1. Start with the original equation:
   \[
   3x - 2y = -12
   \]

2. Subtract \( 3x \) from both sides:
   \[
   -2y = -3x - 12
   \]

3. Divide every term by \( -2 \) to solve for \( y \):
   \[
   y = \frac{-3x}{-2} + \frac{-12}{-2}
   \]

4. Simplify the fractions:
   \[
   y = \frac{3}{2}x + 6
   \]

Thus, the equation in slope-intercept form is:
\[
y = \frac{3}{2}x + 6
\]

### Do you want more details or have any questions?

Here are 5 related questions:
1. How do you determine the slope from an equation in slope-intercept form?
2. What is the significance of the y-intercept in a linear equation?
3. How can you graph the line given by \( y = \frac{3}{2}x + 6 \)?
4. How would you rewrite a line in standard form if it's in slope-intercept form?
5. How do you find the x-intercept of the line \( y = \frac{3}{2}x + 6 \)?

**Tip:** The slope in the slope-intercept form, \( y = mx + b \), is the coefficient of \( x \), which shows how steep the line is.

Learn how to convert the linear equation 3x-2y=-12 into slope-intercept form with a detailed step-by-step guide. This problem covers key algebra concepts like slope-intercept form and solving for y. Suitable for students in Grades 8-10.

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