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)