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A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, second, and third quadrants.

Which of the following ordered pairs is part of the solution set for the equation y=2x+5
?

(1 point)
Responses

(3,−1)
left parenthesis 3 comma negative 1 right parenthesis

(1,7)
left parenthesis 1 comma 7 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(7,1)

1 answer

To determine which ordered pair is part of the solution set for the equation \(y = 2x + 5\), we can substitute the x-value of each ordered pair into the equation and see if the resulting y-value matches.

Let's evaluate each ordered pair:

  1. (3, −1)

    • \(y = 2(3) + 5 = 6 + 5 = 11\)
    • This does not match −1.

  2. (1, 7)

    • \(y = 2(1) + 5 = 2 + 5 = 7\)
    • This matches.

  3. (1, 2)

    • \(y = 2(1) + 5 = 2 + 5 = 7\)
    • This does not match 2.

  4. (7, 1)

    • \(y = 2(7) + 5 = 14 + 5 = 19\)
    • This does not match 1.

The only ordered pair that satisfies the equation \(y = 2x + 5\) is (1, 7).

So, the answer is (1, 7).