Question

Using the graph, derive the equation of the line in slope-intercept form (0,2) (1,-1)

Answer 1

To derive the equation of the line in slope-intercept form \(y = mx + b\) using the points (0, 2) and (1, -1), we follow these steps:

1. **Identify the points:**
- The first point is \((0, 2)\), which gives us the y-intercept \(b\).
- The second point is \((1, -1)\).

2. **Calculate the slope \(m\):**
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in our points \((0, 2)\) and \((1, -1)\):
\[
m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]

3. **Write the equation:**
Now that we have the slope \(m = -3\) and the y-intercept \(b = 2\) (from the point (0, 2)), we can write the equation of the line in slope-intercept form:
\[
y = -3x + 2
\]

Thus, the equation of the line is \(\boxed{y = -3x + 2}\).