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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

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

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

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

(3,45)

1 answer

To determine which ordered pair is part of the solution set for the equation \( y = 4x + 2 \), we can substitute \( x = 3 \) into the equation and calculate the corresponding value of \( y \).

Substituting \( x = 3 \):

\[ y = 4(3) + 2 = 12 + 2 = 14 \]

Now, we can check each given ordered pair to see which one matches:

  1. (3, 12): Here, \( y = 12 \), which does not match \( y = 14 \).
  2. (3, 7): Here, \( y = 7 \), which does not match \( y = 14 \).
  3. (3, 14): Here, \( y = 14 \), which matches perfectly.
  4. (3, 45): Here, \( y = 45 \), which does not match \( y = 14 \).

Thus, the correct option that satisfies the equation \( y = 4x + 2 \) is:

(3, 14).