Tool to calculate a linear equation from 2 points. The equation of a line is written ax + b with a, the direction coefficient (or slope) and b, the y-intercept.

Linear Equation - dCode

Tag(s) : Geometry, Functions

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Tool to calculate a linear equation from 2 points. The equation of a line is written ax + b with a, the direction coefficient (or slope) and b, the y-intercept.

A line of the plane (2D) has an equation of the form $ a x + b $ (affine function), with $ a $ its slope coefficient and $ b $ the y-intercept.

Knowing the slope coefficient and the ordinate at the origin, is deduced the linear equation of the line.

__Example:__ A line of slope coefficient 2 and intercept 3 has the equation $ 2x + 3 $

From 2 points $ A(x_A, y_A) $ and $ B(x_B, y_B) $, the formula for the slope coefficient of the line or segment passing through the points A and B is the result of the fraction: $$ \frac{y_B-y_A}{x_B-x_A} $$

__Example:__ A line passes through 2 points A(1,2) and B(3,4), the slope coefficient is $ \frac{4-2}{3-1} = \frac{2}{2} = 1 $

From the slope coefficient $ a $ and a point $ A(x_A, y_A) $, the computation formula of the y-intercept is the result $ b $ of the equation $$ a x_A + b = y_A $$

__Example:__ A line with slope coefficient $ 3 $ goes through A(2,4), so $ 3 \times 2 + b = 4 \iff b = -2 $, so the y intercept is -2

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