To write the equation of the line in the form \(y = mx + b\), we first need to determine the slope \(m\) using the two points given: \((0, -4)\) and \((2, 1)\).
The slope \(m\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (0, -4)\) and \((x_2, y_2) = (2, 1)\).
Substituting the values:
\[ m = \frac{1 - (-4)}{2 - 0} = \frac{1 + 4}{2} = \frac{5}{2} \]
Now that we have the slope \(m = \frac{5}{2}\), we can use one of the points to find the y-intercept \(b\). Using the point \((0, -4)\):
\[ y = mx + b \] \[ -4 = \frac{5}{2}(0) + b \] \[ -4 = b \]
Now, we have the slope and the y-intercept. Therefore, the equation of the line in \(y = mx + b\) form is:
\[ y = \frac{5}{2}x - 4 \]