To graph the line given by the equation \( y - 6 = -2(x + 9) \), let's first simplify the equation into slope-intercept form (y = mx + b).
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Distribute the -2: \[ y - 6 = -2x - 18 \]
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Add 6 to both sides: \[ y = -2x - 12 \]
Now we have the equation in slope-intercept form, where the slope \( m = -2 \) and the y-intercept \( b = -12 \).
Steps to Graph the Line
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Plot the y-intercept: The y-intercept is at (0, -12). You can start by placing a point at this coordinate on the graph.
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Use the slope: The slope of -2 means that for every 1 unit you move to the right (positive x direction), you move 2 units down (negative y direction).
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Find additional points:
- From the y-intercept (0, -12), move 1 unit to the right to (1, -12) and then down 2 units to (1, -14). Place a point at (1, -14).
- Alternatively, you can also move left from the y-intercept. If you move 1 unit to the left to (-1, -12), then move up 2 units to (-1, -10), placing a point at (-1, -10).
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Draw the line: Connect the points with a straight line extending in both directions.
Example Points to plot
- (0, -12) (y-intercept)
- (1, -14)
- (-1, -10)
Once you've plotted these points and drawn the line, you will have visually represented the equation \( y = -2x - 12 \). If you have access to graphing software or a graph paper, you can use that to make your graph more accurate.