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).
- Calculate the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points:
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)
\[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
- 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 \( b = 2 \).
- 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:
\[ \boxed{y = -3x + 2} \]
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