Choose the correct graph that describes the given linear equation  begin mathsize 20px style bold 2 bold italic y bold minus bold 4 bold italic x bold equals bold 12 end style

To choose the correct graph that describes the given linear equation \( 2y - 4x = 12 \), we need to first convert it into the slope-intercept form (\(y = mx + b\)).

Here are the steps:

1. **Start with the given equation:**
   \[
   2y - 4x = 12
   \]

2. **Isolate \(2y\):**
   \[
   2y = 4x + 12
   \]

3. **Divide everything by 2 to solve for \(y\):**
   \[
   y = 2x + 6
   \]

The slope-intercept form of the equation is \(y = 2x + 6\), where the slope \(m\) is 2 and the y-intercept \(b\) is 6. 

Now, let's analyze the graph based on this information:
- **Slope (\(m\)):** 2 (meaning the line rises 2 units for every 1 unit it runs to the right)
- **Y-intercept (\(b\)):** 6 (meaning the line crosses the y-axis at \(y = 6\))

Therefore, the correct graph will:
1. Cross the y-axis at \(y = 6\).
2. Have a slope of 2, rising steeply.

If you have multiple graph options, you can now look for the graph that meets these criteria. The correct graph will start at the point (0, 6) on the y-axis and have a rise/run ratio of 2/1.

Would you like more details or have any questions?

Here are some questions you might ask next:
1. How do I find the x-intercept of this line?
2. What does the slope of the line represent?
3. How do you graph a linear equation using the slope and y-intercept?
4. Can you show me another example of converting to slope-intercept form?
5. How would you solve the equation if it was \(4x - 2y = 12\) instead?

**Tip:** When graphing linear equations, always identify the slope and y-intercept first, as these will guide you in plotting the line accurately.

Learn how to graph the linear equation 2y - 4x = 12 by converting it to slope-intercept form. This guide explains the steps to find the slope and y-intercept, and how to choose the correct graph based on these values. Ideal for students in Grades 7-9.

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