https://file.aiquickdraw.com/mathbot/file/17290060558046laafw4o.jpg

The equation given is:

\[
y - 1 = -2(x - 2)
\]

Let's first simplify this equation:

\[
y - 1 = -2x + 4
\]

Now add 1 to both sides to solve for \(y\):

\[
y = -2x + 5
\]

This is the equation of the line in slope-intercept form, \(y = mx + b\), where \(m = -2\) is the slope and \(b = 5\) is the y-intercept.

Next, we need to check which of the sets of ordered pairs satisfy this equation. For each pair \((x, y)\), we substitute \(x\) into the equation and see if it results in the corresponding \(y\).

### A. \((0, -2)\) and \((1, 3)\)
- For \((0, -2)\): 
  \[
  y = -2(0) + 5 = 5 \quad (\text{not } -2)
  \]
  This does not satisfy the equation.
  
- For \((1, 3)\):
  \[
  y = -2(1) + 5 = 3
  \]
  This satisfies the equation.

Since one pair fails, option A is incorrect.

### B. \((-1, 7)\) and \((2, 1)\)
- For \((-1, 7)\):
  \[
  y = -2(-1) + 5 = 2 + 5 = 7
  \]
  This satisfies the equation.
  
- For \((2, 1)\):
  \[
  y = -2(2) + 5 = -4 + 5 = 1
  \]
  This satisfies the equation.

Both pairs satisfy the equation, so **option B is correct**.

### C. \((1, 2)\) and \((4, 3)\)
- For \((1, 2)\):
  \[
  y = -2(1) + 5 = 3
  \quad (\text{not } 2)
  \]
  This does not satisfy the equation.

Since one pair fails, option C is incorrect.

### D. \((0, 5)\) and \((-2, 9)\)
- For \((0, 5)\):
  \[
  y = -2(0) + 5 = 5
  \]
  This satisfies the equation.
  
- For \((-2, 9)\):
  \[
  y = -2(-2) + 5 = 4 + 5 = 9
  \]
  This satisfies the equation.

Both pairs satisfy the equation, so **option D is correct**.

### E. \((3, -1)\) and \((2, -1)\)
- For \((3, -1)\):
  \[
  y = -2(3) + 5 = -6 + 5 = -1
  \]
  This satisfies the equation.
  
- For \((2, -1)\):
  \[
  y = -2(2) + 5 = -4 + 5 = 1
  \quad (\text{not } -1)
  \]
  This does not satisfy the equation.

Since one pair fails, option E is incorrect.

### Conclusion:
The correct sets of ordered pairs are:

**B** and **D**.

---

Would you like further details or have any questions about the process?

Here are some additional related questions for practice:
1. How would the equation change if the slope were halved?
2. Can you find the x-intercept of this equation?
3. What would the equation look like if it passed through the point \((3, 4)\)?
4. How does changing the slope affect the steepness of the line?
5. What happens to the equation if the y-intercept is moved to 3?

**Tip:** When checking if points lie on a line, always substitute each point into the equation and verify both sides match.

Select all the sets of ordered pairs that the graph of the equation y - 1 = -2(x - 2) contains.

Identify which sets of ordered pairs satisfy the equation y - 1 = -2(x - 2). This problem involves graphing and verifying ordered pairs on linear equations, suitable for students in Grades 8-10. Learn how to apply slope-intercept form for accurate solutions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation