To find the equation of the line in slope-intercept form (y = mx + b) using the coordinates (1, -1) and (0, 2), we first need to determine the slope (m) of the line.
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, -1) and (0, 2):
- \((x_1, y_1) = (1, -1)\)
- \((x_2, y_2) = (0, 2)\)
Now plug in the values:
\[ m = \frac{2 - (-1)}{0 - 1} = \frac{2 + 1}{0 - 1} = \frac{3}{-1} = -3 \]
Now that we have the slope (m = -3), we can use one of the points to find the y-intercept (b). Let's use the point (0, 2) where \(x = 0\) gives the y-intercept directly.
Thus, \(b = 2\).
Now we can write the equation of the line in slope-intercept form:
\[ y = -3x + 2 \]
So the equation of the line is:
\[ y = -3x + 2 \]