Tool to compute a slope (director coefficient) from 2 points whose coordinates are known in the 2D plane (x-axis and y-axis values).

Slope Coefficient - dCode

Tag(s) : Geometry, Functions

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The slope (director/angular coefficient) of a line indicates the variation of the y-coordinate when the x-coordinate increments of 1 unit.

From 2 points `A(x1,y1)` and `B(x2,y2)`, the slope coefficient of the line or the segment that passes through points `A` and `B` is calculated from the fraction formula: $$ \frac{y2-y1}{x2-x1} $$

__Example:__ Search the slope of an affine function that goes through 2 points (x-axis, y-axis) `A(1,2)` and `B(3,4)`, is calculating the slope value which is $ \frac{4-2}{3-1} = \frac{2}{2} = 1 $

If a line is vertical then the slope coefficient is infinity $ \infty $.

Any line on the plane corresponds to an affine function of equation $ y = ax + b $ with $ a $ the directional coefficient and $ b $ the ordinate at the origin.

After finding the equation of the line from the directing coefficient (see above), then take 2 values for $ x $ (for example $ 0 $ and $ 1 $) and calculate the value of $ y $ for each value . The values $ (x_1, y_1) $ and $ (x_2, y_2) $ are the coordinates of 2 points on the line, connecting them is enough to draw the line.

Two lines are parallel if and only if their slope coefficients are equal.

If 2 lines have the same director coefficient then they are parallel.

Two lines are perpendicular (orthogonal) if and only if the product (multiplication) of their slope coefficients is $ -1 $

If the product (multiplication) of the slope coefficients of 2 lines is $ -1 $, then the 2 lines are orthogonal (perpendicular)

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Cite as source (bibliography):

*Slope Coefficient* on dCode.fr [online website], retrieved on 2023-12-03,

- Slope Coefficient Calculator
- What is the slope coefficient? (Definition)
- How to calculate slope coefficient?
- What is the slope coefficient of a vertical line?
- What is the slope coefficient of a horizontal line?
- How to find the equation of a line with the slope coefficient?
- How to draw a line with the slope coefficient?
- How to demonstrate that 2 lines are parallel?
- How to demonstrate that 2 lines are perpendicular?

coefficient,slope,line,equation,vertical,horizontal,affine,function

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