Why can't a vertical line be written in the form y=mx+b?

It can be written in the same form.

For a vertical line value of x is constant say c, m=1. Hence the equation is y=1*c + b.

Now, as 1*c ad b are constants, their resultant is another constant, say k. Thus the equation becomes y = k. Please note that this is derived from the standard form, as shown above.

In y=mx+b form, the m is the slope (change in y over change in x), and the b is the Y intercept (the y value of the function at the place where the line intersects the y axis.

Where does a vertical line intersect the y axis?

How do you calculate the slope when all of the points on the line have the same x value? (i.e., how can there be a change in x when there is only one x?)

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Scott said, "y=b would form a vertical line."

No, that is the equation of a horizontal line. It is the same as y = 0x+b. Ravindran made the same mistake, "the equation becomes y = k." That's another horizontal line.

The value of y needs to be a constant in order to make a vertical line. y=b would form a vertical line.

b Can not be included in above eqn. because the above line will never intersect y axis,also for a vertical line m must be infinity