To find the slope-intercept form of a line (y = mx + b) from three points, you can follow these steps:
1. **Identify Points**: Start by identifying the three points you are given. Let’s denote them as (x1, y1), (x2, y2), and (x3, y3).
2. **Calculate the Slope (m)**: Choose any two points to calculate the slope using the formula:
m = (y2 – y1) / (x2 – x1)
Use different pairs of points if necessary, ensuring that the slope is consistent.
3. **Find the Y-Intercept (b)**: After determining the slope, you can substitute one of the points and the slope into the slope-intercept equation to solve for b. Using any point (x1, y1), the equation becomes:
y1 = mx1 + b
Solve for b:
b = y1 – mx1
4. **Construct the Equation**: Now that you have both m (slope) and b (y-intercept), plug them into the slope-intercept form:
y = mx + b
5. **Verification**: Optionally, you can verify that the equation holds true for the third point to ensure accuracy.
This method enables you to efficiently derive the slope-intercept form from any three points as long as they are not collinear.