Tool to calculate a right 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 right 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 \( a x + b \), with \( a \) its slope coefficient and \( b \) the y-intercept.

Knowing the slope coefficient and the ordinate at the origin, is deduced the 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: $$ \ frac {y2-y1} {x2-x1} $$

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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