Question

Write an equation that represents this non-proportional linear relationship the coordinates are(-2, -1) (0,1) )2,3)

Answer 1

To find the equation of a non-proportional linear relationship given the points \((-2, -1)\), \((0, 1)\), and \((2, 3)\), we first need to determine the slope of the line using any two of the points.

Let's use the points \((0, 1)\) and \((2, 3)\):

1. **Calculate the slope (m):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1
\]

2. **Use the slope-intercept form \(y = mx + b\) to find the equation:**
Given \(m = 1\), we can substitute \(x = 0\) and \(y = 1\) (from point \((0, 1)\)) to find \(b\):
\[
1 = 1(0) + b \implies b = 1
\]

3. **Write the equation:**
The equation of the line is:
\[
y = 1x + 1 \quad \text{or simply} \quad y = x + 1
\]

4. **Verify with other points:**
For \((-2, -1)\):
\[
y = -2 + 1 = -1 \quad \text{(This point is on the line)}
\]
For \((2, 3)\):
\[
y = 2 + 1 = 3 \quad \text{(This point is also on the line)}
\]

Thus, the equation representing the non-proportional linear relationship of the given coordinates is:
\[
\boxed{y = x + 1}
\]