https://file.aiquickdraw.com/mathbot/file/1726773986950j846exp3.jpg

The equation in the image is \( 3x + 4y = 12 \). To graph this, let's find the intercepts and use them to plot the line.

### Finding the intercepts:
1. **For the x-intercept**: Set \( y = 0 \) in the equation \( 3x + 4y = 12 \).
   \[
   3x + 4(0) = 12 \implies 3x = 12 \implies x = 4
   \]
   So, the x-intercept is \( (4, 0) \).

2. **For the y-intercept**: Set \( x = 0 \) in the equation \( 3x + 4y = 12 \).
   \[
   3(0) + 4y = 12 \implies 4y = 12 \implies y = 3
   \]
   So, the y-intercept is \( (0, 3) \).

### Plotting:
- The x-intercept is \( (4, 0) \).
- The y-intercept is \( (0, 3) \).

To graph the line, plot these two points \( (4, 0) \) and \( (0, 3) \) on the grid and connect them with a straight line.

Let me know if you'd like to see further details, or if you have any other questions! Here are some related questions:

1. How do you find the slope of the line from the equation?
2. How can you rewrite the equation \( 3x + 4y = 12 \) in slope-intercept form?
3. What is the slope of this line, and how does it relate to the intercepts?
4. How would the graph change if the equation were \( 3x + 4y = 8 \)?
5. What are the general steps to graph any linear equation?

**Tip**: When graphing lines, finding both intercepts can quickly provide two key points to sketch the line.

Graph the line represented by the equation 3x + 4y = 12. Select two points on the coordinate grid to represent the x- and y-intercepts. A line will connect the points.

Learn how to graph the linear equation 3x + 4y = 12 by finding the x- and y-intercepts. This tutorial provides a step-by-step guide suitable for students in Grades 7-10. Understand key concepts like linear equations and intercepts.

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