If a horizontal line L is at a distance a from the x-axis then ordinate of every point lying on the line is either a or -a . Therefore , equation of the line L is either y = a or y = – a . Choice of sign will depend upon the position of the line according as the line is above or below the y-axis . Similarly , the equation of a vertical line at a distance b from the y-axis is either x = b or x = – b
Numerical : Find the equations of the lines parallel to axes and passing through ( 2 , 4 ).
Solution : Equation of line parallel to y axis & passing through ( 2,4 ) will be x = 2
Equation of line parallel to x axis & passing through ( 2,4 ) will be y = 4
Point Slope Form
If a fixed point P0 ( x0 , y0 ) & Slope m of line is know , we can write the equation of the line .
Let P ( x , y ) be an arbitrary point on L . Then , y – y0 = m ( x – x0 )