Question

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

Answer 1

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

1. **Calculate the slope (m)**:
The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

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

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

2. **Use one point to find the y-intercept (b)**:
We can use the point (0, 2), the y-intercept is simply \( b = 2 \).

3. **Write the equation**:
Now that we have \( m \) and \( b \), we can write the equation of the line:

\[
y = -3x + 2
\]

Thus, the equation of the line in slope-intercept form is \( y = -3x + 2 \).