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To determine which graph best represents the equation \(3y - 4x = 7\), let's start by rewriting it in slope-intercept form, \(y = mx + b\).

1. Start with the equation:
   \[
   3y - 4x = 7
   \]

2. Solve for \(y\):
   \[
   3y = 4x + 7
   \]

   \[
   y = \frac{4}{3}x + \frac{7}{3}
   \]

The slope (\(m\)) is \(\frac{4}{3}\), and the y-intercept (\(b\)) is \(\frac{7}{3}\).

Now, let's examine the graphs:

- The first graph shows a line with a negative slope, which does not match our equation since the slope should be positive.
- The second graph shows a line with a positive slope that matches the expected slope of \(\frac{4}{3}\).

Therefore, the second graph best represents the equation \(3y - 4x = 7\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you determine the slope and y-intercept from an equation?
2. What is the significance of the slope in the context of a graph?
3. How do you convert standard form equations to slope-intercept form?
4. How can you check if a point lies on the line of a given equation?
5. How do different forms of a line equation (standard, slope-intercept) relate to each other?

**Tip:** When analyzing graphs, always pay attention to the slope and intercept to quickly determine which line corresponds to a given equation.

This page helps you understand how to determine the correct graph that represents the linear equation 3y - 4x = 7. We walk you through converting the equation to slope-intercept form and examining the slope and intercept to match the correct graph. Suitable for students in Grades 8-10.

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