To graph the inequality \( y \ge x - 3 \), follow these steps:
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Identify the Boundary Line: The boundary line for the equation \( y = x - 3 \) can be plotted. This line has a slope of 1 and a y-intercept of -3, meaning it intersects the y-axis at (0, -3) and increases one unit up for each unit it moves to the right.
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Graph the Boundary Line:
- First, plot the points (0, -3) and (3, 0) which come from substituting x = 0 and x = 3 respectively into the equation \( y = x - 3 \).
- Draw a solid line through these points, because the inequality includes equality (the “greater than or equal to” part).
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Determine the Shading: Since the inequality is \( y \ge x - 3 \), you will shade the region above the line. This is because the values of \( y \) are greater than or equal to the values on the line \( y = x - 3 \).
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Final Representation:
- The half-plane above the line is the solution to the inequality.
So your final graph should display a solid line going through points such as (0, -3) and (3, 0), with shading upwards from the line to indicate the area where \( y \) is greater than or equal to \( x - 3 \).
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