To write the equation of the line that passes through the points \((-2, -1)\) and \((0, 1)\), we can use the two-point form of the line equation.
First, we need to find the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (-2, -1)\) and \((x_2, y_2) = (0, 1)\):
\[ m = \frac{1 - (-1)}{0 - (-2)} = \frac{1 + 1}{0 + 2} = \frac{2}{2} = 1 \]
Now that we have the slope \(m = 1\), we can use the point-slope form of the equation of the line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point \((0, 1)\) (you can use either point), we have:
\[ y - 1 = 1(x - 0) \]
This simplifies to:
\[ y - 1 = x \] \[ y = x + 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ \boxed{y = x + 1} \]