When you dilate horizontally you dilate by the inverse of the x quantity. Because your x-quantity is 1/4, you dilate horizontally by 4. You do this by extending the function from the y-axis 4 times its old length. (You multiply the x value of all points on the function by 4)
So a function y=x that has a x coefficient of 1/4 will dilate horizontally by 4, extending the point (1,1) to (4,1), making the line appear much longer and shorter, flatter. You can see that because this is a simple example it relates to slope in a noticeable fashion.
You just make it fatter and shorter *4 in this occasion.
In this case, the order of operations for translating functions doesn't matter.
(The way I do this is draw a light line perpendicular to the y-axis and have it intersect with the function at a whole numbered point, then extend it out to the whole numbered point with 4* its distance from x=0)