y = 5x + 3.....the slope here is 5. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, we flip the original slope and change the sign. So we have slope 5 or 5/1.....flip it and it becomes 1/5....change the sign and it becomes - 1/5. So our perpendicular line will have a slope of -1/5.
y = mx + b
slope(m) = -1/5
(2,2)....x = 2 and y = 2
now we sub into the formula and find b, the y int
2 = -1/5(2) + b
2 = -2/5 + b
2 + 2/5 = b
10/5 + 2/5 = b
12/5 = b
so ur perpendicular equation is : y = -1/5x + 12/5 <==