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To solve this problem, we need to determine which graph represents the equation \( 5x + y = 5 \).

### Steps:
1. **Rearrange the equation** into slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   \[
   5x + y = 5
   \]
   Subtract \( 5x \) from both sides:
   \[
   y = -5x + 5
   \]
   So, the slope \( m = -5 \) and the y-intercept \( b = 5 \).

2. **Interpret the graph**:
   - The slope of \( -5 \) means that for every 1 unit increase in \( x \), \( y \) decreases by 5 units.
   - The y-intercept of 5 means the line crosses the y-axis at \( y = 5 \).

Now, we check the graphs:
- The correct graph should have a line passing through the point \( (0, 5) \) and have a slope of \( -5 \), which is a steep downward line.

### The correct graph:
The **last graph** (fourth option) fits this description:
- It crosses the y-axis at \( y = 5 \).
- It has a steep negative slope consistent with \( m = -5 \).

Thus, the **last graph** represents the equation \( 5x + y = 5 \).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. How can you determine the slope and intercept from a linear equation?
2. What does the slope of a line tell you about its steepness?
3. How can you check if a point lies on a line defined by an equation?
4. What is the general form of a linear equation and how can you convert it?
5. How does the y-intercept affect the position of the line?

**Tip**: Always rearrange linear equations into slope-intercept form to easily interpret the slope and intercept values for graphing.

Which of the following graphs represent the equation 5x + y = 5?

Learn how to solve and graph the linear equation 5x + y = 5. Follow step-by-step instructions to convert the equation into slope-intercept form and analyze the graph. This question is ideal for Grades 8-10 students.

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