The equation you provided is:

$x + y = 3$

This is a linear equation, and the graph will be a straight line. Let's solve it step by step for different values of $x$ and find the corresponding $y$ values.

Step-by-Step Solution:

1. Rearrange the equation to express $y$ in terms of $x$:

   $y = 3 - x$

2. Create a table of values for different values of $x$, and calculate the corresponding $y$ values.

$x$	$y = 3 - x$
0	$3 - 0 = 3$
1	$3 - 1 = 2$
2	$3 - 2 = 1$
-1	$3 - (-1) = 4$
-2	$3 - (-2) = 5$

So, the corresponding points $(x, y)$ are:

• $(0, 3)$
• $(1, 2)$
• $(2, 1)$
• $(-1, 4)$
• $(-2, 5)$

3. Plot these points on a graph.

Now you can draw a straight line through these points to represent the equation $x + y = 3$.

Steps to Graph:

1. Draw the Cartesian plane with the x-axis and y-axis.
2. Plot the points: (0, 3), (1, 2), (2, 1), (-1, 4), and (-2, 5).
3. Connect these points with a straight line.

This line represents the equation $x + y = 3$.

Would you like more details on how to draw the graph, or have any other questions?

Related Questions:

1. What is the slope of the line $x + y = 3$?
2. How do you find the x-intercept and y-intercept of a linear equation?
3. How would the graph change if the equation was $x + y = 5$?
4. Can you write the equation in slope-intercept form?
5. How do you check if a point lies on the line of the equation $x + y = 3$?

Tip:

To graph a line easily, always find the x- and y-intercepts first by setting $x = 0$ and $y = 0$, then plot those points.