To identify the correct graph that represents the equation $x + y = 3$, we will first analyze the equation and then compare it with the graphs provided.

Analyzing the Equation $x + y = 3$:

1. Rewrite in Slope-Intercept Form: $y = -x + 3$ This is a straight line with a slope of $-1$ and a y-intercept of $3$.

2. Key Points:

   • When $x = 0$, $y = 3$. So, the point $(0, 3)$ is on the line.
   • When $y = 0$, $x = 3$. So, the point $(3, 0)$ is on the line.

Identifying the Correct Graph:

• The line should pass through the points $(0, 3)$ and $(3, 0)$.
• The slope of the line is $-1$, meaning it decreases by 1 unit in $y$ for every 1 unit increase in $x$.

Checking the Graphs:

• Graph A: Shows a line that seems to pass through $(0, 3)$ and $(3, 0)$, with a negative slope.
• Graph B: The line passes through $(0, -3)$, which is incorrect.
• Graph C: The line has a negative slope but passes through $(0, -3)$, which is incorrect.
• Graph D: The line has a positive slope, which is incorrect for this equation.

Conclusion:

The correct graph is Graph A, as it accurately represents the equation $x + y = 3$.

Do you want more details or have any questions?

Here are 5 related questions:

1. How would you graph the equation $y = 2x - 1$?
2. What does the slope of a line represent in a graph?
3. How would the graph change if the equation were $x - y = 3$?
4. How can you determine if two lines are parallel by looking at their equations?
5. What is the significance of the y-intercept in the context of a linear equation?

Tip: When graphing a linear equation, always start by identifying key points, like intercepts, and use the slope to determine the direction of the line.