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To find the coordinates \( A \), \( B \), and \( C \) on the line \( y = x - 7 \) using the table of values, we follow these steps:

1. The line equation given is \( y = x - 7 \).
2. We have the \( x \) values from the table: \( -1 \), \( 0 \), and \( 1 \).
3. We need to find the corresponding \( y \) values for these \( x \) values using the equation \( y = x - 7 \).

Let's calculate the \( y \) values for each \( x \):

- For \( x = -1 \):
  \[
  y = -1 - 7 = -8
  \]
  So, the coordinate \( A \) is \((-1, -8)\).

- For \( x = 0 \):
  \[
  y = 0 - 7 = -7
  \]
  So, the coordinate \( B \) is \((0, -7)\).

- For \( x = 1 \):
  \[
  y = 1 - 7 = -6
  \]
  So, the coordinate \( C \) is \((1, -6)\).

Thus, the coordinates are:

- \( A = (-1, -8) \)
- \( B = (0, -7) \)
- \( C = (1, -6) \)

Would you like more details or have any questions about these calculations?

Here are five related questions for further practice:
1. What would be the coordinate of a point on the line \( y = x - 7 \) if \( x = 2 \)?
2. How would the equation change if the line was shifted up by 3 units?
3. What is the slope of the line \( y = x - 7 \)?
4. Find the coordinates of a point on the line \( y = 2x - 7 \) for \( x = -1 \).
5. What is the \( y \)-intercept of the line \( y = x - 7 \)?

**Tip:** To determine the slope and intercept of a linear equation in the form \( y = mx + b \), \( m \) represents the slope and \( b \) represents the \( y \)-intercept.

A, B, and C are coordinates on the line y = x - 7. Use the table of values to find A, B, and C.

Learn how to find the coordinates A, B, and C on the line y = x - 7 using a table of values. This problem covers key algebraic concepts such as linear equations and coordinate geometry, suitable for students in Grades 6-8.

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