Question

Use the table to answer the question.

x
y

−2
−1

0 1
2 3
Write an equation that represents this nonproportional linear relationship.

(1 point)
Responses

y=x+2
y equals x plus 2

y=12x+1
y equals Start Fraction 1 over 2 End Fraction x plus 1

y=x+1
y equals x plus 1

y=−2x+1

Answer 1

To find the equation representing the given points in a nonproportional linear relationship, we can start by identifying a linear equation in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

The points provided are:
- (-2, -1)
- (0, 1)
- (2, 3)

We can start by determining the slope \(m\) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 1) and (2, 3):

\[
m = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1
\]

So the slope \(m = 1\).

Next, we can find the y-intercept \(b\) by plugging in the point (0, 1):

\[
y = mx + b \Rightarrow 1 = 1(0) + b \Rightarrow b = 1
\]

Thus, the equation of the line is:

\[
y = 1x + 1 \quad \text{or} \quad y = x + 1
\]

Based on the options provided, the correct response is:

**y = x + 1**.