Tool to calculate a linear equation from 1 or 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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Linear Equation
Linear Equation Calculator (2D plane)
Answers to Questions (FAQ)
What is a linear equation? (Definition)
A linear equation is a mathematical relationship that describes a straight line in a 2D plane. It is usually in the form $ y = ax + b $ (or $ f(x) = ax + b $), where $ a $ and $ b $ are real numbers and $ x $ is the variable.
How to calculate the equations of a line?
The equation on the right, of the form $ a x + b $ (affine function), has 2 parameters: $ a $ its slope coefficient and $ b $ the ordinate at the origin.
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 $
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: $$ \frac{y_B-y_A}{x_B-x_A} $$
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 $
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
How to find the equation of a line from two points?
It is possible to find the equation directly from the formula: $$ y = \frac{ (x - x_A)(y_B - y_A) }{ (x_B - x_A) } + y_A $$
How to find the equation of a line from one point and the slope?
For a point $ P = (x_1, y_1) $ and a slope $ S $, the calculation formula is: $$ y = S(x - x_1) + y_1 $$
Source code
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- Linear Equation Calculator (2D plane)
- What is a linear equation? (Definition)
- How to calculate the equations of a line?
- How to calculate slope coefficient?
- How to calculate the y intercept?
- How to find the equation of a line from two points?
- How to find the equation of a line from one point and the slope?
