Find the equation of the line with the slope undefined and the x - intercept (2,0)

Question

Find the equation of the line with the slope undefined and the x - intercept (2,0)

Answer 1

When the slope of a line is undefined, the line is a vertical one.  This is because a vertical is infinitely steep, you cannot determine the slope of that line.  When the line is vertical, every point on that line has the same x-coordinate.

 

The x-intercept is (2, 0).  This means that the line crosses the x-axis at x=2.  Therefore, the equation of the line is

 

x = 2

Answer 2

The equation of a line may be expressed in Standard Form, slope-intercept form, point-slope form, etc.

 

In slope-intercept form, y= mx + b, m=slope and b is the y-intercept (y-value when x=0).  The slope m is undefined for a vertical line.

 

However, the line may still be expressed in Standard From, Ax + By = C.  Since the slope is -A/B, a value of B=0 means that the slope is undefined; this leaves the equation as Ax = C.

 

The x-intercept (x-value when y=0) is C/A.  The problem gives the x-intercept as (2,0).  So, C/A=2.

 

Putting this point into the Standard Form equation Ax = C, we get the equation of the line:

   x = C/A

   x = 2