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Slope Coefficient

Tool to compute a slope from 2 points. The slope coefficient of a line indicates the variation of the y-coordinate when the x-coordinate increments of 1 unit.

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Slope Coefficient -

Tag(s) : Geometry, Functions

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# Slope Coefficient

## Slope Coefficient Calculator

### How to calculate slope coefficient?

From 2 points A(x1,y1) and B(x2,y2), the slope coefficient of the line or the segment hat 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 an horizontal line?

If a line is vertical then the slope coefficient is $0$. This is sometimes the case of a tangeant 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 coeffifients 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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