To find the equation of the line in slope-intercept form (y = mx + b) using the given points, we can first calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
The points given are (0, 1) and (1, -4). Let's use these points:
- \( (x_1, y_1) = (0, 1) \)
- \( (x_2, y_2) = (1, -4) \)
Now, we can plug in the values:
\[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]
So the slope \( m = -5 \).
Now we use the slope-intercept form equation \( y = mx + b \) and substitute \( m \) and one of the points to find \( b \). We'll use the point (0, 1):
\[ y = mx + b \] \[ 1 = -5(0) + b \] \[ 1 = 0 + b \] \[ b = 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -5x + 1 \]
So the correct answer is:
D. y = -5x + 1