What is the equation of the line that goes through (2, 2) and is perpendicular to y = 5x + 3?

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 <==