Question
The graph represents y = 5x − 3. Which statements are true about the graph?
Responses
A The coordinate pair (0, 3) represents a point on the graph and a solution to the equation.The coordinate pair (0, 3) represents a point on the graph and a solution to the equation.
B The coordinate pair (2, 7) represents a point on the graph and a solution to the equation.The coordinate pair (2, 7) represents a point on the graph and a solution to the equation.
C The coordinate pair (0, −3) represents a point on the graph and a solution to the equation.The coordinate pair (0, −3) represents a point on the graph and a solution to the equation.
D The coordinate pair (2, −7) represents a point on the graph.The coordinate pair (2, −7) represents a point on the graph.
E The coordinate pair (−1, −4) is a solution to the equation.
Answers
GPT-4o mini
To determine which statements are true for the equation \(y = 5x - 3\), we can evaluate each coordinate pair given in the responses by substituting the x-values into the equation and checking if the resulting y-value matches.
1. **Coordinate pair (0, 3)**:
- Substitute \(x = 0\):
\[
y = 5(0) - 3 = -3
\]
- The point is (0, -3), so this is **false**.
2. **Coordinate pair (2, 7)**:
- Substitute \(x = 2\):
\[
y = 5(2) - 3 = 10 - 3 = 7
\]
- The point is (2, 7), so this is **true**.
3. **Coordinate pair (0, -3)**:
- Substitute \(x = 0\):
\[
y = 5(0) - 3 = -3
\]
- The point is (0, -3), so this is **true**.
4. **Coordinate pair (2, -7)**:
- Substitute \(x = 2\):
\[
y = 5(2) - 3 = 10 - 3 = 7
\]
- The point is (2, 7), not (2, -7), so this is **false**.
5. **Coordinate pair (-1, -4)**:
- Substitute \(x = -1\):
\[
y = 5(-1) - 3 = -5 - 3 = -8
\]
- The point is (-1, -8), so this is **false**.
### Summary of True Statements:
- B: The coordinate pair (2, 7) represents a point on the graph and a solution to the equation. **(True)**
- C: The coordinate pair (0, -3) represents a point on the graph and a solution to the equation. **(True)**
So, the true statements are **B** and **C**.
1. **Coordinate pair (0, 3)**:
- Substitute \(x = 0\):
\[
y = 5(0) - 3 = -3
\]
- The point is (0, -3), so this is **false**.
2. **Coordinate pair (2, 7)**:
- Substitute \(x = 2\):
\[
y = 5(2) - 3 = 10 - 3 = 7
\]
- The point is (2, 7), so this is **true**.
3. **Coordinate pair (0, -3)**:
- Substitute \(x = 0\):
\[
y = 5(0) - 3 = -3
\]
- The point is (0, -3), so this is **true**.
4. **Coordinate pair (2, -7)**:
- Substitute \(x = 2\):
\[
y = 5(2) - 3 = 10 - 3 = 7
\]
- The point is (2, 7), not (2, -7), so this is **false**.
5. **Coordinate pair (-1, -4)**:
- Substitute \(x = -1\):
\[
y = 5(-1) - 3 = -5 - 3 = -8
\]
- The point is (-1, -8), so this is **false**.
### Summary of True Statements:
- B: The coordinate pair (2, 7) represents a point on the graph and a solution to the equation. **(True)**
- C: The coordinate pair (0, -3) represents a point on the graph and a solution to the equation. **(True)**
So, the true statements are **B** and **C**.