Straight Lines

Slope (Gradient) of a Line

The slope 'm' measures the steepness of a line and is calculated as the tangent of the angle of inclination or the change in y divided by the change in x between two points.

Point-Slope Form

An equation of a line passing through a given point (x1, y1) with a given slope m is expressed as y - y1 = m(x - x1).

Two-Point Form

When coordinates of two distinct points (x1, y1) and (x2, y2) on a line are known, its equation is found using y - y1 = [(y2 - y1) / (x2 - x1)] * (x - x1).

Slope-Intercept Form

The equation of a line with slope m and y-intercept c is given by the standard linear relationship y = mx + c.

Normal Form

The equation of a line when the perpendicular distance from the origin (p) and the angle (alpha) made by this perpendicular with the positive x-axis are known is x cos(alpha) + y sin(alpha) = p.

Distance of a Point from a Line

The perpendicular distance d from a given point (x1, y1) to the line Ax + By + C = 0 is calculated using the formula |Ax1 + By1 + C| / sqrt(A^2 + B^2).