## Straight line equations (first degree)

- Ax +By +C = 0( General form)
- x=0. (Y-axis)
- y =0 (x-axis)
- x = a (Parallel to y-axis)
- y = b (Parallel to x axis)
- The distance of a point (x ,y) from x-axis is |y| and from y-axis |x|.
- Y=mx +c. Line which cuts off an intercept c on y-axis and makes an angle θ with the positive direction (anticlockwise) of x-axis and tanθ = m is called its slope or gradient.
- y = m x. Any line through the origin.
- (x/a)+(y/b) = 1. Intercept form: Here a and b are the intercepts on the axis of the x and y respectively.
- In this case the position AB of the line intercepts between the axes is the length √(a
^{2 }+b^{2 }) by Pythagoras rule.
- y-y
_{1 }= m(x-x_{1 }). Equation of straight line through a given point (x_{1 }, y_{1 }) and having slope m i.e. tanθ=m.
- Note: (y-y
_{1 })/(x-x_{1 })=m. If m=0 i.e. the line is parallel to to x- axis, then its equation will be Nr = 0 or y-y_{1 }=0. If m = ∞i.e. the line is perpendicular to x-axis, then its equation will be Dr=0 or x-x_{1 }=0.
- Y-y
_{1 }=[(y_{2 }-y_{1 })/(x_{2 }-x_{1 })](x-x_{1 })Equation of a straight line passing through two given points(x_{1 }, y_{1 }) and (x_{2 }, y_{2 }).
- Xcos α +ysin α = p. equation of a line on which the length of perpendicular from origin is p and α is the angle which this perpendicular makes with the positive direction of x-axis.
- Parametric form of a straight line: (x-x
_{1 })/cosθ=(y-y_{1 })/sinθ=r this is another form