Question

Consider the linear equation y=2x+1
. Which of the following ordered pairs is a solution to the equation?(1 point)
Responses

(2, 5)
open paren 2 comma 5 close paren

(−3, 7)
open paren negative 3 comma 7 close paren

(4, −9)
open paren 4 comma negative 9 close paren

(1, 2)

Answer 1

To determine which ordered pair is a solution to the equation \( y = 2x + 1 \), we need to substitute the x-values from each pair into the equation and see if we get the corresponding y-value.

1. For \( (2, 5) \):
\[
y = 2(2) + 1 = 4 + 1 = 5 \quad \text{(matches the y-value)}
\]

2. For \( (-3, 7) \):
\[
y = 2(-3) + 1 = -6 + 1 = -5 \quad \text{(does not match)}
\]

3. For \( (4, -9) \):
\[
y = 2(4) + 1 = 8 + 1 = 9 \quad \text{(does not match)}
\]

4. For \( (1, 2) \):
\[
y = 2(1) + 1 = 2 + 1 = 3 \quad \text{(does not match)}
\]

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