Question content area top left
Part 1
For the​ equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
x minus y equals 3
Question content area bottom left
Part 1
Complete the table below.
x
y

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Given the equation \( x - y = 3 \), we need to find three ordered pair solutions by completing the table. Let's solve for \( y \) in terms of \( x \):

\[ x - y = 3 \implies y = x - 3 \]

Now, let's choose three different values for \( x \) and find the corresponding \( y \) values:

1. \( x = 0 \):
   \[ y = 0 - 3 = -3 \]
   So, the ordered pair is \( (0, -3) \).

2. \( x = 3 \):
   \[ y = 3 - 3 = 0 \]
   So, the ordered pair is \( (3, 0) \).

3. \( x = 6 \):
   \[ y = 6 - 3 = 3 \]
   So, the ordered pair is \( (6, 3) \).

Now, let's complete the table:

| \( x \) | \( y \) |
|--------|--------|
| 0      | -3     |
| 3      | 0      |
| 6      | 3      |

Next, to graph the equation, we'll plot the points \((0, -3)\), \((3, 0)\), and \((6, 3)\) on a coordinate plane and draw a line through them.

Here are the details and steps to plot these points and draw the graph:

1. Plot the point \((0, -3)\) on the coordinate plane.
2. Plot the point \((3, 0)\) on the coordinate plane.
3. Plot the point \((6, 3)\) on the coordinate plane.
4. Draw a straight line passing through these three points. This line represents the equation \( x - y = 3 \).

Would you like a detailed explanation or have any questions about this process? 

Here are five questions you might want to ask next:
1. How do you graph a linear equation with only one variable given?
2. What is the slope-intercept form of a linear equation?
3. How do you find the slope of a line given two points?
4. Can you explain how to determine if a point lies on a given line?
5. How can you convert a linear equation into standard form?

**Tip:** When plotting points, always double-check their coordinates to ensure they satisfy the original equation. This helps to avoid mistakes in graphing.

Explore how to graph the equation x - y = 3 by finding ordered pairs and plotting them on a coordinate plane. This problem involves solving linear equations and understanding coordinate geometry concepts. Suitable for Grades 6-8.

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