Straight Lines in a cartesian plane is described algebraically by linear equations.

Slope of a Line

Slope (m) of a non-vertical line passing through the points (x1, y1) and (x2, y2) is given by

m = (y2 - y1)/(x2 - x1)

If a line makes an angle α with the positive direction of x-axis, then the slope of the line is given by m = tan α. Slope of horizontal line is zero and slope of vertical line is undefined.

Parallel and Perpendicular Lines

Two lines are parallel if and only if their slopes are equal. Two lines are perpendicular if and only if product of their slopes is -1.

Collinear Points

Three points A, B and C are collinear, if and only if slope of AB = slope of BC.

Equation of Line

Equation of the horizontal line having distance a from the x-axis is either y = a or y = - a.

Equation of the vertical line having distance b from the y-axis is either x = b or x = - b.

Slope Intercept Form

The point (x, y) on the line with slope m and y-intercept c:

y = mx + c

Two Point Form

Equation of the line passing through the points (x1, y1) and (x2, y2) is given by

y - y1 = {(y2 - y1)/{x2 - x1)}(x - x1)

Point Slope Form

The point (x, y) lies on the line with slope m and through the fixed point (x1, y1):

y - y1 = m(x - x1)

Intercept Form

Equation of a line making intercepts a and b on the x-and y-axis respectively:

x/a + y/b = 1