The graph represents y = 5x − 3. Which statements are true about the graph?

Question

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.

Answer 1

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.