Question

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)

Answer 1

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)**.