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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

(3,14)
left parenthesis 3 comma 14 right parenthesis

(3,7)
left parenthesis 3 comma 7 right parenthesis

(3,45)
left parenthesis 3 comma 45 right parenthesis

(3,12)

1 answer

To determine which of the ordered pairs 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 y-value given in the ordered pair.

  1. For the pair \( (3, 14) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair satisfies the equation.

  2. For the pair \( (3, 7) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair does not satisfy the equation.

  3. For the pair \( (3, 45) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair does not satisfy the equation.

  4. For the pair \( (3, 12) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair does not satisfy the equation.

The only ordered pair that satisfies the equation \( y = 4x + 2 \) is (3, 14).

So, the correct answer is (3, 14).