The graph of the equation y = x − 6 is shown. Which THREE statements are correct?
Responses
A The coordinate pair (8, 3) represents a point on the graph and a solution to the equation.The coordinate pair (8, 3) represents a point on the graph and a solution to the equation.
B The coordinate pair (5, −1) represents a point on the graph and a solution to the equation.The coordinate pair (5, −1) represents a point on the graph and a solution to the equation.
C The coordinate pair (3, −3) represents a point on the graph and a solution to the equation.The coordinate pair (3, −3) represents a point on the graph and a solution to the equation.
D The coordinate pair (−1, −7) represents a point on the graph and a solution to the equation.The coordinate pair (−1, −7) represents a point on the graph and a solution to the equation.
E The coordinate pair (−3, −8) represents a point on the graph and a solution to the equation.The coordinate pair (−3, −8) represents a point on the graph and a solution to the equation.
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Answered by
GPT-4o mini
To find out which coordinate pairs are solutions to the equation \( y = x - 6 \), we can substitute the x-values of each coordinate pair into the equation and see if the corresponding y-value is correct.
1. **A:** (8, 3)
- Substitute \( x = 8 \):
\[
y = 8 - 6 = 2
\]
- The point (8, 3) does NOT satisfy the equation since \( y = 3 \) is not equal to 2.
2. **B:** (5, -1)
- Substitute \( x = 5 \):
\[
y = 5 - 6 = -1
\]
- The point (5, -1) satisfies the equation.
3. **C:** (3, -3)
- Substitute \( x = 3 \):
\[
y = 3 - 6 = -3
\]
- The point (3, -3) satisfies the equation.
4. **D:** (-1, -7)
- Substitute \( x = -1 \):
\[
y = -1 - 6 = -7
\]
- The point (-1, -7) satisfies the equation.
5. **E:** (-3, -8)
- Substitute \( x = -3 \):
\[
y = -3 - 6 = -9
\]
- The point (-3, -8) does NOT satisfy the equation since \( y = -8 \) is not equal to -9.
The correct statements are:
- **B:** The coordinate pair (5, -1) represents a point on the graph and a solution to the equation.
- **C:** The coordinate pair (3, -3) represents a point on the graph and a solution to the equation.
- **D:** The coordinate pair (-1, -7) represents a point on the graph and a solution to the equation.
So the three correct statements are **B**, **C**, and **D**.
1. **A:** (8, 3)
- Substitute \( x = 8 \):
\[
y = 8 - 6 = 2
\]
- The point (8, 3) does NOT satisfy the equation since \( y = 3 \) is not equal to 2.
2. **B:** (5, -1)
- Substitute \( x = 5 \):
\[
y = 5 - 6 = -1
\]
- The point (5, -1) satisfies the equation.
3. **C:** (3, -3)
- Substitute \( x = 3 \):
\[
y = 3 - 6 = -3
\]
- The point (3, -3) satisfies the equation.
4. **D:** (-1, -7)
- Substitute \( x = -1 \):
\[
y = -1 - 6 = -7
\]
- The point (-1, -7) satisfies the equation.
5. **E:** (-3, -8)
- Substitute \( x = -3 \):
\[
y = -3 - 6 = -9
\]
- The point (-3, -8) does NOT satisfy the equation since \( y = -8 \) is not equal to -9.
The correct statements are:
- **B:** The coordinate pair (5, -1) represents a point on the graph and a solution to the equation.
- **C:** The coordinate pair (3, -3) represents a point on the graph and a solution to the equation.
- **D:** The coordinate pair (-1, -7) represents a point on the graph and a solution to the equation.
So the three correct statements are **B**, **C**, and **D**.
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