Search for a tool
Slope Coefficient

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

Results

Slope Coefficient -

Tag(s) : Geometry, Functions

Share dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Slope Coefficient' tool for free! Thank you!

# Slope Coefficient

## Slope Coefficient Calculator

### What is the slope coefficient? (Definition)

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

### How to calculate slope coefficient?

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

### What is the slope coefficient of a vertical line?

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

### What is the slope coefficient of a horizontal line?

If a line is vertical then the slope coefficient is $0$. This is sometimes the case of a tangent or an asymptote.

### How to find the equation of a line with the slope coefficient?

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.

### How to draw a line with the slope coefficient?

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.

### How to demonstrate that 2 lines are parallel?

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.

### How to demonstrate that 2 lines are perpendicular?

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)

## Source code

dCode retains ownership of the "Slope Coefficient" source code. Except explicit open source licence (indicated Creative Commons / free), the "Slope Coefficient" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Slope Coefficient" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Slope Coefficient" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

## Cite dCode

The copy-paste of the page "Slope Coefficient" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Slope Coefficient on dCode.fr [online website], retrieved on 2023-12-03, https://www.dcode.fr/slope-coefficient

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!