Write an equation of the line through (3,-5) and perpendicular to 3y=x-6

3y = x - 6
y = 1/3x - 2. 
slope her is 1/3. A perpendicular line will have anegative reciprocal slope. To find the negative reciprocal of a number, u flip the number and change the sign. So the slope we need os -3/1 or just -3.(see how I flipped the slope and changed the sign)

y = mx + b
slope(m) = -3
(3,-5)...x = 3 and y = -5
now we sub and find b, the y int
-5 = -3(3) + b
-5 = -9 + b
-5 + 9 = b
4 = b

so ur perpendicular equation is : y = -3x + 4