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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)
left parenthesis 3 comma 12 right parenthesis

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 value of y matches the y-value of the ordered pair.

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

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

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

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

The only ordered pair that satisfies the equation is \( (3, 14) \).

Therefore, the correct response is: (3, 14)