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Question

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

(3,12)
left parenthesis 3 comma 12 right parenthesis

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

(3,45)

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 pair into the equation and see if the resulting \( y \)-value matches the one given in the pair.

  1. For \( (3, 14) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair is a solution.

  2. For \( (3, 12) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair is not a solution.

  3. For \( (3, 7) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair is not a solution.

  4. For \( (3, 45) \): \[ y = 4(3) + 2 = 12 + 2 = 14 \] This pair is not a solution.

Thus, the only ordered pair that is part of the solution set for the equation \( y = 4x + 2 \) is:

(3, 14).