To determine the set of ordered pairs that satisfy the equation \( y - 1 = -2(x - 2) \), we can first rewrite the equation in slope-intercept form (the form \( y = mx + b \)).
Starting with the original equation:
\[ y - 1 = -2(x - 2) \]
Distributing the \(-2\) on the right side:
\[ y - 1 = -2x + 4 \]
Now, add 1 to both sides to isolate \(y\):
\[ y = -2x + 4 + 1 \]
This simplifies to:
\[ y = -2x + 5 \]
Now that we have the equation in slope-intercept form, we can identify the slope as \(-2\) and the y-intercept as \(5\). This line will contain ordered pairs of the form \((x, y)\), where \(y\) is a function of \(x\).
To find specific ordered pairs, we can plug in some values for \(x\) and calculate the corresponding \(y\):
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If \(x = 0\): \[ y = -2(0) + 5 = 5 \quad \Rightarrow \quad (0, 5) \]
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If \(x = 1\): \[ y = -2(1) + 5 = 3 \quad \Rightarrow \quad (1, 3) \]
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If \(x = 2\): \[ y = -2(2) + 5 = 1 \quad \Rightarrow \quad (2, 1) \]
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If \(x = 3\): \[ y = -2(3) + 5 = -1 \quad \Rightarrow \quad (3, -1) \]
Here are a few ordered pairs that satisfy the equation \(y = -2x + 5\):
- \((0, 5)\)
- \((1, 3)\)
- \((2, 1)\)
- \((3, -1)\)
Thus, the set of ordered pairs that satisfy the equation \(y - 1 = -2(x - 2)\) includes \((0, 5)\), \((1, 3)\), \((2, 1)\), and \((3, -1)\), among others. Any pair of the form \((x, -2x + 5)\) for any real value of \(x\) will also be a solution.
If you have specific options provided to select from, please provide those options, and I can help identify which ones are correct.