Select the option below that correctly shows which of the following ordered pairs is part of the solution set for the equation y=4x+2 .(1 point) Responses (3,12) left parenthesis 3 comma 12 right parenthesis (3,7) left parenthesis 3 comma 7 right parenthesis (3,45) left parenthesis 3 comma 45 right parenthesis (3,14)

1 answer

To determine which ordered pair is part of the solution set for the equation \( y = 4x + 2 \), we can substitute the \( x \)-value from each ordered pair into the equation and see if the resulting \( y \)-value matches the one in the ordered pair.

The equation is \( y = 4x + 2 \).

For each ordered pair:

  1. (3, 12): \[ y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(not a solution)} \]

  2. (3, 7): \[ y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(not a solution)} \]

  3. (3, 45): \[ y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(not a solution)} \]

  4. (3, 14): \[ y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(solution)} \]

The only ordered pair that is part of the solution set for the equation \( y = 4x + 2 \) is (3, 14).