Question
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Answer
To graph the equation \( y = -x + 3 \), plot the y-intercept at \( (0, 3) \). Then, use the slope of -1 to find another point by moving 1 unit right and 1 unit down to \( (1, 2) \). Draw a straight line through these points.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To graph the linear equation \( y=-x+3 \), start by identifying two key points. When \( x=0 \), then \( y=3 \) (the y-intercept). When \( x=3 \), \( y=0 \) (the x-intercept). Plot these points, (0,3) and (3,0), on your graph. Then, connect them with a straight line, extending in both directions. Remember, the line represents all the solutions to the equation! A fun way to check your work is to pick a random value of \( x \) and see if your line holds up! For instance, if you choose \( x=1 \), plugging it in gives \( y=-1+3=2 \), so the point (1,2) should sit nicely on your line. Happy graphing!
