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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

(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

(1,2)

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 and see if the corresponding y-value matches.

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

  2. For the ordered pair \((3, -1)\): \[ y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(This is incorrect, y should be -1)} \]

  3. For the ordered pair \((7, 1)\): \[ y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(This is incorrect, y should be 1)} \]

  4. For the ordered pair \((1, 2)\): \[ y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(This is incorrect, y should be 2)} \]

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

So, the correct response is \((1, 7)\).