if y=12x+7 were changed to y=12x+2, how would the graph of the new function compare with its original

see explanation

Step-by-step explanation:

The equation of a line in slope - intercept form is

y = mx + c (m is the slope and c the y - intercept)

y = 12x + 7 ← is in this form

with m = 12 and c = 7

y = 12x + 2 ← is also in this form

with m = 12 and c = 2

Since the slopes are equal the lines are parallel

c = 7 → c = 2 is a vertical translation of 5 units down

In comparison the line y = 12x + 2 is parallel to y = 12x + 7

and translated