Question

Use the image to answer the question.
(0, 2), (1, -1)
Write the equation of the line in slope-intercept form.
__

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) using the two points provided: (0, 2) and (1, -1).

1. **Calculate the slope \( m \)**:

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

Substituting the coordinates of the points:

- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)

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

2. **Use one of the points to find the y-intercept \( b \)**. We can use the point (0, 2), which is particularly convenient since it gives us the y-intercept directly:

At \( x = 0 \), \( y = 2 \), so \( b = 2 \).

3. **Write the equation in slope-intercept form**:

Now that we have the slope \( m = -3 \) and the y-intercept \( b = 2 \), we can write the equation:

\[
y = -3x + 2
\]

So the equation of the line in slope-intercept form is:

\[
\boxed{y = -3x + 2}
\]