To derive the equation of the line in slope-intercept form (y = mx + b) using the points (1, 8) and (0, 4), we'll follow these steps:
-
Find the slope (m): The slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let \( (x_1, y_1) = (1, 8) \) and \( (x_2, y_2) = (0, 4) \): \[ m = \frac{4 - 8}{0 - 1} = \frac{-4}{-1} = 4 \]
-
Use the slope and one of the points to find the y-intercept (b): We can use the y-intercept point (0, 4) which suggests that when \( x = 0 \), \( y = 4 \). Thus, \( b = 4 \).
-
Write the equation: Now, we can plug the slope and y-intercept into the slope-intercept form: \[ y = mx + b \] Substituting \( m = 4 \) and \( b = 4 \): \[ y = 4x + 4 \]
Thus, the equation of the line in slope-intercept form is: \[ y = 4x + 4 \]