To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) using the two points given: (1, -4) and (0, 1).
Step 1: Calculate the slope (m)
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points (1, -4) and (0, 1):
\[ m = \frac{1 - (-4)}{0 - 1} = \frac{1 + 4}{-1} = \frac{5}{-1} = -5 \]
Step 2: Use point-slope form to find the equation
We can use the slope \( m = -5 \) and one of the points to find the equation. We'll use the point (0, 1):
The general form of a line equation is:
\[ y - y_1 = m(x - x_1) \]
Plugging in the point (0, 1):
\[ y - 1 = -5(x - 0) \] \[ y - 1 = -5x \] \[ y = -5x + 1 \]
Step 3: Writing the final equation
The equation of the line in slope-intercept form is:
\[ y = -5x + 1 \]
Matching with options:
Comparing with the given options, the correct answer is:
D. y = -5x + 1