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The problem asks which graph represents the equation \( -8x + 5y = 32 \).

To determine the correct graph, let's first rewrite the equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Solve for \( y \)
Starting with:
\[
-8x + 5y = 32
\]
Add \( 8x \) to both sides:
\[
5y = 8x + 32
\]
Now, divide by 5:
\[
y = \frac{8}{5}x + \frac{32}{5}
\]

### Step 2: Interpret the slope and intercept
- The slope is \( \frac{8}{5} \), which means the line rises by 8 units for every 5 units it moves to the right.
- The y-intercept is \( \frac{32}{5} \), or 6.4.

### Step 3: Analyze the graphs
- The correct graph should have a y-intercept at approximately 6.4 and a slope of \( \frac{8}{5} \).

Looking at the graphs:
- **Graph A**: The slope is negative and does not match the calculated slope.
- **Graph B**: This graph has a steep slope and a large y-intercept but does not match the positive slope of \( \frac{8}{5} \).
- **Graph C**: This graph has a positive slope and a y-intercept near 6.4. Let's check if the slope matches \( \frac{8}{5} \), and it seems correct.
- **Graph D**: The slope is steeper than \( \frac{8}{5} \).

### Conclusion:
**Graph C** represents the equation \( -8x + 5y = 32 \) because it has the correct slope and y-intercept.

Would you like further explanation or have any questions?

Here are 5 related questions to deepen understanding:
1. How do you find the slope of a line from two points on a graph?
2. What is the significance of the y-intercept in a linear equation?
3. How does changing the slope affect the steepness of a line?
4. What happens to the graph of a line if you change the y-intercept?
5. How can you verify a graph represents an equation by substituting points?

**Tip**: Always convert equations to slope-intercept form \( y = mx + b \) when analyzing graphs!

Which of the following graphs represents the equation -8x + 5y = 32?

Learn how to determine which graph represents the linear equation -8x + 5y = 32 by converting it to slope-intercept form. Analyze the slope and y-intercept to match the correct graph. Suitable for students in Grades 8-10.

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