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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

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

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

1 answer

To determine which ordered pair is part of the solution set for the equation \( y = 2x + 5 \), we can substitute the x-values of each ordered pair into the equation to see if it yields the corresponding y-values.

  1. For the ordered pair \( (3, -1) \): \[ y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(not -1)} \]

  2. For the ordered pair \( (1, 7) \): \[ y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(this is correct)} \]

  3. For the ordered pair \( (7, 1) \): \[ y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(not 1)} \]

  4. For the ordered pair \( (1, 2) \): \[ y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(not 2)} \]

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

Therefore, the correct answer is: (1, 7).