The equation $x + y = 2$ represents a straight line on a Cartesian coordinate plane. To graph this equation, follow these steps:

Steps to graph the equation $x + y = 2$:

1. Rearrange the equation to solve for $y$: $y = -x + 2$ This is now in slope-intercept form, $y = mx + b$, where:

   • The slope $m = -1$
   • The y-intercept $b = 2$

2. Plot the y-intercept: Start by plotting the point where the line intersects the y-axis. This happens when $x = 0$. From the equation, when $x = 0$, $y = 2$. So, plot the point (0, 2).

3. Use the slope to find another point: The slope is -1, which means for every 1 unit increase in $x$, $y$ decreases by 1 unit. From the point (0, 2), move 1 unit to the right (increasing $x$ by 1) and 1 unit down (decreasing $y$ by 1), which gives you the point (1, 1).

4. Draw the line: Plot these points, (0, 2) and (1, 1), then draw a straight line through them.

The graph:

The graph is a straight line passing through the points (0, 2) and (1, 1). The line slopes downward from left to right.

Would you like further details on this or help with a specific aspect of the graph?

Here are 5 related questions:

1. What is the slope-intercept form of a linear equation?
2. How do you interpret the slope and intercept in the equation $y = -x + 2$?
3. How can you find the x-intercept of the line $x + y = 2$?
4. How does changing the slope of a line affect its graph?
5. What are some methods to solve for the equation of a line given two points?

Tip: When graphing a line, plotting at least two points is essential. You can always extend the line in both directions using the slope!