https://file.aiquickdraw.com/mathbot/file/1728613387074o16283xy.jpg

Let's review your work based on the image you uploaded, where you have the equation:

\[
8x - 12y = -24
\]

### Step-by-Step Analysis:

#### Finding the x-intercept:
- To find the **x-intercept**, you set \( y = 0 \) and solve for \( x \).
  \[
  8x - 12(0) = -24 \implies 8x = -24 \implies x = \frac{-24}{8} = -3
  \]
- Therefore, the x-intercept is \( (-3, 0) \).

#### Finding the y-intercept:
- To find the **y-intercept**, you set \( x = 0 \) and solve for \( y \).
  \[
  8(0) - 12y = -24 \implies -12y = -24 \implies y = \frac{-24}{-12} = 2
  \]
- Therefore, the y-intercept is \( (0, 2) \).

#### Conclusion:
- Your intercepts are correctly calculated: 
  - x-intercept: \( (-3, 0) \)
  - y-intercept: \( (0, 2) \)
  
From the notes on the graph, it looks like you have plotted the points correctly too.

Would you like any further details or clarifications? Here are 5 related questions to expand on this concept:

1. How would you rewrite the equation in slope-intercept form \( y = mx + b \)?
2. What is the slope of the line based on the intercepts you calculated?
3. Can you find a third point on the line to confirm the accuracy of your graph?
4. How would you check your solution by substituting the intercept points into the original equation?
5. What would happen if the equation had a positive constant on the right-hand side (e.g., \( 8x - 12y = 24 \))?

**Tip**: Always substitute the intercepts back into the original equation to verify that they satisfy it.

Learn how to solve the linear equation 8x - 12y = -24 by finding the x- and y-intercepts. This problem walks through key concepts like graphing and intercept calculations. Suitable for students in Grades 8-10.

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