Which equation gives the rule for this table?
Understand the Problem
The question asks us to identify the equation that corresponds to the relationship between $x$ and $y$ as defined in the provided table of values. We need to determine which equation is valid for all $(x, y)$ pairs listed in the table.
Answer
$y = -2x$
Answer for screen readers
$y = -2x$
Steps to Solve
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Test the first point (3, -6) with each equation
- $y = -3x - 6$: $-6 = -3(3) - 6 \Rightarrow -6 = -9 - 6 \Rightarrow -6 = -15$. This is false.
- $y = -3x$: $-6 = -3(3) \Rightarrow -6 = -9$. This is false.
- $y = -2x - 6$: $-6 = -2(3) - 6 \Rightarrow -6 = -6 - 6 \Rightarrow -6 = -12$. This is false.
- $y = -2x$: $-6 = -2(3) \Rightarrow -6 = -6$. This is true.
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Test the second point (4, -8) with the remaining equation
We only need to test $y = -2x$ since it was the only equation that worked for the first point.
- $y = -2x$: $-8 = -2(4) \Rightarrow -8 = -8$. This is true.
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Test the third point (5, -10) with the remaining equation
We only need to test $y = -2x$ since it was the only equation that worked for the first two points.
- $y = -2x$: $-10 = -2(5) \Rightarrow -10 = -10$. This is true.
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Test the fourth point (6, -12) with the remaining equation
We only need to test $y = -2x$ since it was the only equation that worked for the first three points.
- $y = -2x$: $-12 = -2(6) \Rightarrow -12 = -12$. This is true.
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Conclusion
Since the equation $y = -2x$ is valid for all $(x, y)$ pairs in the table, we have found the correct equation.
$y = -2x$
More Information
The equation represents a linear relationship where $y$ is always $-2$ times the value of $x$.
Tips
A common mistake is to only check the first point and assume that the equation that works for the first point is the correct one. It's important to check all points in the table to ensure that the equation holds true for all given values.
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