To graph the equation \( x + y = -1 \), follow these steps:
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Rearrange the equation: You can rewrite the equation in slope-intercept form (y = mx + b): \[ y = -x - 1 \]
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Identify the slope and y-intercept: In the equation \( y = -x - 1 \):
- The slope (m) is \(-1\).
- The y-intercept (b) is \(-1\), which means the line crosses the y-axis at the point (0, -1).
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Plot the y-intercept: Start by plotting the point (0, -1) on the graph.
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Use the slope to find another point: From the y-intercept (0, -1), use the slope to find another point. Since the slope is \(-1\), you can go down 1 unit and to the right 1 unit:
- From (0, -1), move down to (1, -2). Plot this point.
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Draw the line: Connect the two points with a straight line.
Your graph will look like a straight line that descends from the left to the right, crossing the y-axis at (0, -1) and the x-axis at (-1, 0).
Summary of Points to Plot
- (0, -1) — y-intercept
- (1, -2) — another point from the slope
You can also find the x-intercept by setting \( y = 0 \): \[ x + 0 = -1 \implies x = -1 \] Thus, the x-intercept is (-1, 0).
Now you have three points: (0, -1), (1, -2), and (-1, 0) to plot on your graph!