If you wanted to shift the graph of y=4x+7 down , which equation could you use ?

Well, the function is written in y = mx + b, which is slope intercept form.  If the graph were to shift down, you would reduce "b" by the number of units that you want to shift.

Therefore for the specific question you posted, and assuming your shift is "k" units - the equation would be ---

y = 4x + (b + k)

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.