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