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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

(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)
left parenthesis 7 comma 1 right parenthesis

Answer 1

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 resulting y-value matches the y-value in the ordered pair.

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

2. For the ordered pair $(1,7)$: $$y=2(1)+5=2+5=7\text{(this is a match)}$$

3. For the ordered pair $(1,2)$: $$y=2(1)+5=2+5=7\text{(not 2)}$$

4. For the ordered pair $(7,1)$: $$y=2(7)+5=14+5=19\text{(not 1)}$$

Thus, the only ordered pair that is part of the solution set for the equation $y=2x+5$ is $(1,7)$.