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Question

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

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

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

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

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

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

1. For \( (1, 2) \): \[ y = 2(1) + 5 = 2 + 5 = 7 \] So, \( (1, 2) \) does not satisfy the equation.

2. For \( (1, 7) \): \[ y = 2(1) + 5 = 2 + 5 = 7 \] So, \( (1, 7) \) satisfies the equation.

3. For \( (3, -1) \): \[ y = 2(3) + 5 = 6 + 5 = 11 \] So, \( (3, -1) \) does not satisfy the equation.

4. For \( (7, 1) \): \[ y = 2(7) + 5 = 14 + 5 = 19 \] So, \( (7, 1) \) does not satisfy the equation.

The only ordered pair that is part of the solution set for the equation \( y = 2x + 5 \) is \( \boxed{(1, 7)} \).