To graph the equation \( y = \frac{1}{2}x + 2 \), we follow these steps:
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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 \( m = \frac{1}{2} \) and the y-intercept \( b = 2 \).
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Plot the y-intercept.
- The y-intercept is the point where the line crosses the y-axis. For this equation, the y-intercept is \( (0, 2) \).
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Use the slope to find another point.
- The slope \( \frac{1}{2} \) means that for every 2 units you move up (rise), you move 1 unit to the right (run).
- Starting from the y-intercept \( (0, 2) \), if you move 1 unit to the right (to \( x = 1 \)), then move up \( \frac{1}{2} \) units to place a point at \( (1, 2.5) \).
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Draw the line.
- Plot the two points \( (0, 2) \) and \( (1, 2.5) \) on a coordinate plane.
- Draw a straight line through these points, extending it in both directions.
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Add more points if necessary.
- For additional accuracy, you can find more points by choosing different values of \( x \) and calculating the corresponding \( y \). For instance:
- If \( x = 2 \), \( y = \frac{1}{2}(2) + 2 = 3 \) (point \( (2, 3) \))
- If \( x = -2 \), \( y = \frac{1}{2}(-2) + 2 = 1 \) (point \( (-2, 1) \))
- For additional accuracy, you can find more points by choosing different values of \( x \) and calculating the corresponding \( y \). For instance:
By following these steps, you can accurately sketch the line represented by the equation \( y = \frac{1}{2}x + 2 \). If you were to visualize this graphically, you would see a straight line that rises from left to right, crossing the y-axis at 2 and having a gentle upward slope.