Slope Coefficient

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: $$ \frac{y2-y1}{x2-x1} $$

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

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

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)