Graph the linear equation: \( y=-x+3 \)

While I can't create a graph directly, I can guide you through the process of graphing the linear equation \( y = -x + 3 \). ### Step-by-Step Guide to Graphing \( y = -x + 3 \) 1. **Identify the Slope and Y-Intercept**: - The equation is in the 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 \( b = 3 \). 2. **Plot the Y-Intercept**: - Start by plotting the y-intercept on the graph. This is the point where the line crosses the y-axis. - For \( b = 3 \), plot the point \( (0, 3) \). 3. **Use the Slope to Find Another Point**: - The slope of \( -1 \) means that for every 1 unit you move to the right (positive x-direction), you move 1 unit down (negative y-direction). - From the point \( (0, 3) \), move 1 unit to the right to \( (1, 3) \) and then 1 unit down to \( (1, 2) \). Plot this point. 4. **Draw the Line**: - Connect the two points \( (0, 3) \) and \( (1, 2) \) with a straight line. Extend the line in both directions. 5. **Label the Axes**: - Make sure to label the x-axis and y-axis for clarity. ### Summary of Points - Points to plot: \( (0, 3) \) and \( (1, 2) \). You can use graph paper or a graphing tool to visualize this linear equation. The line will slope downwards from left to right due to the negative slope.