https://file.aiquickdraw.com/mathbot/file/1725460049422yvlcz2ox.jpg

To solve this problem, we need to determine which of the given points satisfies the linear equation \( y = 2x - 9 \).

### Steps to solve:

1. **Substitute each point** \((x, y)\) into the equation \( y = 2x - 9 \).
2. **Check if the equation holds true** for each point.

#### Checking each option:

1. **Point (2, 4):**
   \[
   y = 2x - 9 \quad \Rightarrow \quad 4 = 2(2) - 9 \quad \Rightarrow \quad 4 = 4 - 9 \quad \Rightarrow \quad 4 \neq -5 \quad \text{(False)}
   \]

2. **Point (4, -1):**
   \[
   y = 2x - 9 \quad \Rightarrow \quad -1 = 2(4) - 9 \quad \Rightarrow \quad -1 = 8 - 9 \quad \Rightarrow \quad -1 = -1 \quad \text{(True)}
   \]

3. **Point (-2, -13):**
   \[
   y = 2x - 9 \quad \Rightarrow \quad -13 = 2(-2) - 9 \quad \Rightarrow \quad -13 = -4 - 9 \quad \Rightarrow \quad -13 = -13 \quad \text{(True)}
   \]

4. **Point (-1, -12):**
   \[
   y = 2x - 9 \quad \Rightarrow \quad -12 = 2(-1) - 9 \quad \Rightarrow \quad -12 = -2 - 9 \quad \Rightarrow \quad -12 \neq -11 \quad \text{(False)}
   \]

### Conclusion:
The points **(4, -1)** and **(-2, -13)** are solutions to the equation \( y = 2x - 9 \).

Would you like to explore this further, or do you have any questions? Here are some related questions you might find useful:

1. How do you determine if a point lies on a given line?
2. What is the slope-intercept form of a linear equation?
3. How can you graph the equation \( y = 2x - 9 \)?
4. What does the slope of the line \( y = 2x - 9 \) represent?
5. How would you find the x-intercept and y-intercept of the equation \( y = 2x - 9 \)?

**Tip:** When solving for points on a line, substitute the \( x \) value into the equation and see if the resulting \( y \) value matches the point's \( y \) coordinate.

The linear equation y = 2x - 9 is given. Which of the following points is a solution of the equation?

Explore how to identify solutions to the linear equation y = 2x - 9. This problem involves checking which points satisfy the equation, using algebraic substitution. Ideal for students in Grades 6-8.

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