Line from Two Points

Implement a function to compute the parameters of a line given two points. The concept of fitting a line to a set of points is fundamental in Model Fitting and Optimization, particularly in the context of RANSAC, where it's used to robustly estimate the parameters of a model from noisy data.

To find the line parameters, we can use the slope-intercept form of a line, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Given two points $(x_1, y_1)$ and $(x_2, y_2)$ , we can calculate the slope $m$ as the ratio of the difference in $y$ -coordinates to the difference in $x$ -coordinates.

Calculate the difference in $y$ -coordinates and $x$ -coordinates between the two points.
Compute the slope $m$ using the differences calculated in step 1.
Use one of the points to solve for the y-intercept $b$ .

m = \frac{y_2 - y_1}{x_2 - x_1}, \quad b = y_1 - m \cdot x_1

This technique is widely used in computer vision applications, such as line detection in images.

Example:

Input:

line_from_points((0,0), (2,4))

Output:

[2.0, 0.0]

Reasoning:

First, compute the slope using $m = \frac{y_2 - y_1}{x_2 - x_1}$ : $m = \frac{4 - 0}{2 - 0} = \frac{4}{2} = 2.0$
Then, compute the intercept using $b = y_1 - m \cdot x_1$ : $b = 0 - 2.0 \cdot 0 = 0.0$
So the function returns the line parameters as $[m, b] = [2.0, 0.0]$

Constraints:

Assume x1 ≠ x2 (non-vertical line)
Return [m, b] rounded to 4 decimal places

Example:

Constraints:

Test Results