Given the function f(x)=x-2m+2 what is m if the graph of the function does not intersect x axis? x>0

If the graph of the function (which is a line) does not
intercept the x axis, that means that the equation of the line has no real
solutions.

In other words, there are no such values for x
to cancel the equation of the line.

When the graph is
intercepting x axis, then y = 0.

Let f(x) =
y.

Since the graph is not intercepting x axis, then y
> 0 =>

x-2m+2 >
0

We'll isolate x to the left
side:

x > 2m - 2

Since
x > 0 => 2m - 2 > 0

We'll divide by
2:

m - 1 > 0

m >
1

The interval of possible values for m, for
the graph of f(x) not to intercept x axis, is: (1 ,
+infinite).