To graph the proportional relationship represented by the equation \( y = -2x \), we can plot several points that satisfy this equation. The equation tells us that for every unit increase in \( x \), \( y \) will decrease by 2 units.
Let's calculate some points by substituting different \( x \) values:
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For \( x = -2 \): \[ y = -2(-2) = 4 \quad \Rightarrow \quad (-2, 4) \]
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For \( x = -1 \): \[ y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2) \]
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For \( x = 0 \): \[ y = -2(0) = 0 \quad \Rightarrow \quad (0, 0) \]
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For \( x = 1 \): \[ y = -2(1) = -2 \quad \Rightarrow \quad (1, -2) \]
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For \( x = 2 \): \[ y = -2(2) = -4 \quad \Rightarrow \quad (2, -4) \]
Now we have the following points:
- (-2, 4)
- (-1, 2)
- (0, 0)
- (1, -2)
- (2, -4)
Plotting the Points
- Mark the point (-2, 4) on the graph.
- Mark the point (-1, 2) on the graph.
- Mark the point (0, 0) on the graph.
- Mark the point (1, -2) on the graph.
- Mark the point (2, -4) on the graph.
Drawing the Line
Once you have plotted these points, draw a straight line through them. The line should extend infinitely in both directions.
Properties of the Graph
- The line will slope downwards from left to right, indicating a negative relationship.
- Because it is a proportional relationship passing through the origin, it will cross the y-axis at (0, 0).
- The slope of the line is -2, indicating that for every increase of 1 in \( x \), \( y \) decreases by 2.
This is how you can graph the equation \( y = -2x \).
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