Ask a New Question
Menu

Use the image to answer the 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

(1,7)
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

(3,−1)

1 answer

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

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

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

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

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

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