Question

If the value of x increases by 4 ,how does the value of m(x-5) change

Answer 1

I'm going to assume that you're discussing the linear function y = mx + b.  If that's not it, please provide more information on the function you're studying.

y = mx + b has a graph that is the straight line through (0,b) with slope m.

y = m(x-5) + b has a graph which is parallel to the previous graph, but intersects the x-axis at a different point.

Examples:  start with y = mx + b
Suppose we have      y = 3x + 2   to work with
The graph intersects the y-axis at (0,2).  It intersects the x-axis where y=0=3x+2, or at x = -2/3  => (-2/3, 0)

Now modify y = 3x + 2 by replacing "x" with "x-5."  the graph of this "new" function f(x) = 3(x-5) + 2 is parallel to the original graph, but lies 5 units to the right of the original graph.  Both lines have slope 3.

In this case, if x increases by 4 (as your problem states), y will increase by 3(4), or 12, units.

If we go back to y = m(x-5), we see that the graph of this function intersects the x-axis at x=5, and this graph has the (unknown) slope m.

If x increases by 4, y increases by (m)(4), or 4m.