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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

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

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

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

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

1 answer

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

Let's check each option:

  1. For (3, 7):

    • Substitute \( x = 3 \): \[ y = 4(3) + 2 = 12 + 2 = 14 \]
    • The ordered pair (3, 7) does not satisfy the equation.

  2. For (3, 14):

    • Substitute \( x = 3 \): \[ y = 4(3) + 2 = 12 + 2 = 14 \]
    • The ordered pair (3, 14) satisfies the equation.

  3. For (3, 12):

    • Substitute \( x = 3 \): \[ y = 4(3) + 2 = 12 + 2 = 14 \]
    • The ordered pair (3, 12) does not satisfy the equation.

  4. For (3, 45):

    • Substitute \( x = 3 \): \[ y = 4(3) + 2 = 12 + 2 = 14 \]
    • The ordered pair (3, 45) does not satisfy the equation.

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