Question

Use the image to answer the question. 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), follow these steps:

1. **Identify the points:**
Point 1: \( (0, 2) \)
Point 2: \( (1, -1) \)

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

3. **Use the slope and one point to find the y-intercept (b):**
Using the slope-intercept form \( y = mx + b \) and the point \( (0, 2) \):
\[
2 = -3(0) + b \implies b = 2
\]

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

So, the equation of the line in slope-intercept form is:
\[
y = -3x + 2
\]