Graph the line. \( y=x \)

To graph the line represented by the equation \( y = x \), follow these steps: 1. **Identify the Slope and Y-Intercept**: The equation \( y = x \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m = 1 \) and the y-intercept \( b = 0 \). 2. **Plot the Y-Intercept**: Start by plotting the y-intercept on the graph. Since \( b = 0 \), the point is (0, 0). 3. **Use the Slope**: The slope of 1 means that for every 1 unit you move to the right (positive x-direction), you move 1 unit up (positive y-direction). From the point (0, 0), you can plot another point: - Move 1 unit right to (1, 1). - You can also move 1 unit left to (-1, -1) to plot another point. 4. **Draw the Line**: Connect the points you plotted with a straight line. The line will extend infinitely in both directions. 5. **Label the Axes**: Make sure to label the x-axis and y-axis for clarity. The resulting graph is a straight line that passes through the origin (0, 0) and has a 45-degree angle with both the x-axis and y-axis, indicating that for every increase in x, y increases by the same amount. If you were to visualize it, it would look like this: ``` | 2 | / | / 1 | / | / 0 |-----/----- | / -1 | / | / -2 | / | ---------------- -2 -1 0 1 2 ``` This is a simple representation of the line \( y = x \).