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 $

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 tangeant 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.

Two lines are perpendicular if and only if the product of their slope coeffifients is -1.