slope is (47 - 15) / (7 - 1) = 16/3
we have equation in the form y = mx + b so m = 16/3 so
y = 16/3 x + b
we know that (1,15) is on this line.
(1,15) on the line means when x = 1, y = 15 so plug and chugg
15 = (16/3)*1 + b
15 - 16/3 = b
45/3 - 16/3 = b
b = 29/3
so your equation looks like
y = (16)/(3)x + (29)/(3)