Question

What equation translates y=(x) by 8 units to the right ?

Answer 1

We are given with an original equation of y = x where the slope is 1 and passes through (0,0). if the equation is translated by 8 units to the right, the line still has the same slope but now passes through (8,0). 
y-y1 = m (x-x1)y - 0 = 1 (x-8)y = x - 8
The line now becomes y = x - 8