Use the table to answer the question.

Question

x
y
−2
−1
0 1
2 3

Write an equation that represents this nonproportional linear relationship.
(1 point)
Responses

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
y equals negative 2 x plus 1
y=x+2

Answer 1

To determine the equation that represents the nonproportional linear relationship given the points in the table, we can first find the slope (m) of the line using any two points from the table. The points are:

1. (-2, -1)
2. (0, 1)
3. (2, 3)

Let's use the points (0, 1) and (2, 3) to find the slope.

The formula for the slope (m) is:

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

Using the points (0, 1) (let's call this (x1, y1)) and (2, 3) (let's call this (x2, y2)):

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

Now that we have the slope, we can use the point-slope form of the linear equation, which is:

\[ y - y_1 = m(x - x_1) \]

Using the point (0, 1):

\[ y - 1 = 1(x - 0) \]

Simplifying this gives:

\[ y - 1 = x \] \[ y = x + 1 \]

Now we can compare this equation to the response options. The correct equation is:

y = x + 1