# How can we write an equation for a line that does not go pass the y-axis ? What would the "b" in the equation be ?

gsenviro | Certified Educator

The slope intercept form of a line is given as :

y = mx + b

where, m is the slope of the line and b is the y-intercept (value of y when x = 0, or when line crosses the y-axis).

If a line does not intersect y-axis, then it is parallel to y-axis or perpendicular to the x-axis. In this case, at every point of the line, the y-coordinate will be equal to 0.

Hence, for a line that does not intersect the y-axis, the value of y-intercept (b) would always be 0.

Similarly, the slope of the line will be undefined, since the slope is given as (y2-y1)/(x2-x1) or, (y2-y1)/0.

In fact, the slope-intercept form of the line equation does not work for this particular case: case of a vertical line.

Hope this helps.

ishpiro | Certified Educator

If a line does not intersect y-axis, it means that it is a vertical line with the equation x = C (for example, x = 2 or x = -3.) As mentioned above, it is not possible to put an equation of the vertical line into a slope-intercept form because its slope is undefined.

However, it is not true that the value of b, or y-intercept of a vertical line is 0. The vertical line simply does not have a y-intercept (because it does not cross the y-axis at any point.) Each point on a vertical line has a different value of y, while values of x are the same for every point. For example, the line

x = 2 contains the points (2, -10), (2, 0), (2, 1), (2, 5) and so on.