Question

The graph of the equation y − 1 = −2(x − 2) contains which set(s) of ordered pairs? Select all that apply.

Answer 1

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 \(y\):

1. If \(x = 0\):
\[
y = -2(0) + 5 = 5 \quad \Rightarrow \quad (0, 5)
\]

2. If \(x = 1\):
\[
y = -2(1) + 5 = 3 \quad \Rightarrow \quad (1, 3)
\]

3. If \(x = 2\):
\[
y = -2(2) + 5 = 1 \quad \Rightarrow \quad (2, 1)
\]

4. 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.