1. Lines parallel to the axes (a) Parallel to the x-axis
y (0, c) y = c
x
A line parallel to the x-axis has a slope of 0. So m = 0 in y = mx + c means y = c (constant) for all values of x.
Every point on this line has the same y co-ordinate. y = c is the equation of a line parallel to the x-axis through (0, c).
Therefore, the equation of the x-axis is y = 0 as it passes through (0, 0). (b) Parallel to the y-axis
y x = a
(a, 0)
x
A line parallel to the y-axis has a slope of infi nity (∞). Every point on this line has the same x co-ordinate. x = a is the equation of a line parallel to the y-axis through (a, 0). Therefore, the equation of the y-axis is x = 0 as it passes through (0, 0).
EXAMPLE 5
Write down the equations of the lines h, k, l, x, y.
