Inclination of a line (θ) is the angle that a line makes with the positive direction of x–axis. It is measured in the anticlockwise direction.
Slope of a line is the tangent of the inclination of the line i.e. m = tanθ is the slope of a line whose inclination is θ.
Suppose, P(x1, y1) and Q(x2, y2) are the two points that lie on a line . The slope of the line is tanθ = (y2 – y1)/(x2 – x1)
Two lines with slopes m1 and m2 are parallel if and only if their slopes are equal
i.e. m1 = m2.
Two lines with slopes m1 and m2 are perpendicular if and only if their slopes are negative reciprocal of each other or their product is –1 i.e. m1m2 = –1.
The acute angle (say θ) between the two lines l1 and l2 with slopes m1 and m2 is
tanθ = |(m2 – m1)/(1 + m1m2)| such that 1 + m1m2 ≠ 0.
Three points P, Q and R on the coordinate plane are said to be collinear if
Slope of PQ = Slope of QR
The equation of the horizontal line having distance a from the x–axis is either y = a
or y = –a.
The equation of the vertical line having distance b from the y–axis is either x = b
or x = –b.
Point-slope form of a line is (y – y1) = m(x – x1) where m is the slope of the line passing through the fixed point (x1, y1).
Two-point form of a line passing through two fixed points (x1, y1) and (x2, y2) is
(y – y1) = [(y2 – y1)/(x2 – x1)] (x – x1)
Slope-intercept form of a line having slope m and y–intercept c is y = mx + c and
for x–intercept d, equation of line is y = m(x –d).
Intercept form of a line making intercepts a and b on the x–axis and y–axis, respectively, is (x/a) + (y/b) = 1.
Any equation of the form Ax + By + C = 0 is called the general equation of the line given that A and B both are not simultaneously zero.
The three lines are said to be concurrent if the intersection point of the two lines is also a solution of the third line.
Keywords: distance between two lines, intersection point of two lines, normal form of a line