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.
-
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.
-
B: (5, -1)
- Substitute \( x = 5 \): \[ y = 5 - 6 = -1 \]
- The point (5, -1) satisfies the equation.
-
C: (3, -3)
- Substitute \( x = 3 \): \[ y = 3 - 6 = -3 \]
- The point (3, -3) satisfies the equation.
-
D: (-1, -7)
- Substitute \( x = -1 \): \[ y = -1 - 6 = -7 \]
- The point (-1, -7) satisfies the equation.
-
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.