Question

X -12 0 2
Y -1 1 3

Write an equation that represents this nonproportional linear relationship.

(1 point)

y=x+2

y=-2x+1

y=x+1

y = 1/2x+1

Answer 1

To find the equation that represents the nonproportional linear relationship given the points \( (-12, -1) \), \( (0, 1) \), and \( (2, 3) \), we first need to determine the slope \( m \) of the line.

1. Calculate the slope \( m \) using two of the points. Let's use \( (0, 1) \) and \( (2, 3) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1
\]

2. Now we have the slope \( m = 1 \). We can use the point-slope form of the equation of a line to find the y-intercept \( b \):

Using the point \( (0, 1) \):

\[
y = mx + b
\]

Substitute \( m \) and the coordinates of the point:

\[
1 = 1(0) + b \implies b = 1
\]

Therefore, the equation of the line is:

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

From the options given, the correct equation that represents this nonproportional linear relationship is:

**y = x + 1**.