To find the equation of the line in slope-intercept form (y = mx + b) using the given coordinates (1, -4) and (0, 1), we first need to calculate the slope (m).
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, -4) as \((x_1, y_1)\) and (0, 1) as \((x_2, y_2)\):
\[ m = \frac{1 - (-4)}{0 - 1} = \frac{1 + 4}{0 - 1} = \frac{5}{-1} = -5 \]
Now that we have the slope \( m = -5 \), we can use one of the points to find the y-intercept \( b \). We'll use the point (0, 1), which is particularly useful since it already represents the y-intercept.
In the slope-intercept form, the equation is:
\[ y = mx + b \]
Substituting \( m = -5 \) and \( b = 1 \):
\[ y = -5x + 1 \]
So, the equation of the line in slope-intercept form is:
\[ y = -5x + 1 \]