Straight line equations

Straight line equations (first degree)

1. Ax +By +C = 0( General form)


2. x=0. (Y-axis)


3. y =0 (x-axis)


4. x = a (Parallel to y-axis)


5. y = b (Parallel to x axis)


6. The distance of a point (x ,y) from x-axis is |y| and from y-axis |x|.


7. 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.


8. y = m x. Any line through the origin.


9. (x/a)+(y/b) = 1. Intercept form: Here a and b are the intercepts on the axis of the x and y respectively.


10. In this case the position AB of the line intercepts between the axes is the length √(a² +b² ) by Pythagoras rule.


11. y-y₁ = m(x-x₁ ). Equation of straight line through a given point (x₁ , y₁ ) and having slope m i.e. tanθ=m.


12. Note: (y-y₁ )/(x-x₁ )=m. If m=0 i.e. the line is parallel to to x- axis, then its equation will be Nr = 0 or y-y₁ =0. If m = ∞i.e. the line is perpendicular to x-axis, then its equation will be Dr=0 or x-x₁ =0.


13. Y-y₁ =[(y₂ -y₁ )/(x₂ -x₁ )](x-x₁ )Equation of a straight line passing through two given points(x₁ , y₁ ) and (x₂ , y₂ ).


14. 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.


15. Parametric form of a straight line:  (x-x₁ )/cosθ=(y-y₁ )/sinθ=r this is another form