Question

Write an equation in slope-intercept form for the graph shown.



A coordinate plane with a line passing through points (0, 2) and (1, negative 1)

Answer 1

To write the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

1. **Identify the points:**
- The line passes through the points (0, 2) and (1, -1).

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

3. **Identify the y-intercept (b):**
The y-intercept is the value of y when x = 0. From the point (0, 2), we see that:
\[
b = 2
\]

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

Thus, the equation in slope-intercept form for the line is:
\[
\boxed{y = -3x + 2}
\]