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Linear Equation

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.

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Linear Equation -

Tag(s) : Geometry, Functions

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Linear Equation

Linear Equation Calculator

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.

How to calculate the equations of a line?

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 $$2x + 3$$

How to calculate slope coefficient?

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 $$\frac{4-2}{3-1} = \frac{2}{2} = 1$$

How to calculate the y intercept?

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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