To derive the equation of the line in slope-intercept form (y = mx + b) using the points (0, 2) and (1, -1), follow these steps:
-
Identify the points:
Point 1: \( (0, 2) \)
Point 2: \( (1, -1) \) -
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 in the points:
\[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \] -
Use the slope and one point to find the y-intercept (b):
Using the slope-intercept form \( y = mx + b \) and the point \( (0, 2) \):
\[ 2 = -3(0) + b \implies b = 2 \] -
Write the equation of the line:
Now that we have the slope \( m = -3 \) and the y-intercept \( b = 2 \), we can write the equation of the line:
\[ y = -3x + 2 \]
So, the equation of the line in slope-intercept form is: \[ y = -3x + 2 \]