1. The equation of a line parallel to x-axis is of the form y = k.
The equation of a line parallel to y axis is of the form x = k, where k is a constant.
2. If a line makes an angle θ with the positive direction of x-axis and θ ≠π/2, then the slope of the line is given by tan θ.
3. the slope of a line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1), provided x1≠x2.
4. If two lines have finite slopes m1 and m2
then they are parallel iff m1 = m2
they are perpendicular iff m1*m2 = -1
5. The equation of a line having slope m and y intercept c is y = mx+c
6. The equation of a line having slope m and passing through (x1,y1) is
(y-y1) = m(x-x1)
7. The equation of a line having slope m and passing through (x1,y1)and (x2,y2) is
(y-y1)/(x-x1) = (y1-y2)/(x1-x2)
8.The equation of a line making non-zero intercepts and b on the x and y axes respectively is
(x/a) + (y/b) = 1
9. The equation of a line such that the perpendicular drawn from the origin to the line has length p and inclination α is
x cos α + y sin α = p.
10. The general equation of a line is of the form ax +by +c = o and its slope is –a/b, provided b≠0.
11. If m1 and m2 are the slopes of two lines, then the acute angle θ between them is given by tan θ = |m1-m2|/|1 + m1*m2|, provided m1*m2≠-1.
12. The perpendicular distance of (x1,y1) from the line ax+by+c = 0 is given by |ax1 + by1 + c|/| √(a² + b²)|
13. The point of intersection of two lines, which are not parallel, can be found by solving their equations simultaneously.
14. Family of lines
If u ≡ a1x + b1y +c1 = 0 and
v≡ a2x +b2y +c2 = 0
the u + kv = 0, k Є R represents a family of lines
(i) if u and v are intersecting lines, then u + kv = 0, k Є R represents a family of lines passing through the point of intersection of u =0 and v=0.
(ii) if u and v are two parallel lines, u + kv = 0, k Є R represents a family of straight lines parallel to u =0 and v=0.