What is the equation of the line that passes through (-9,12) and is perpendicular to the line whose equation is y=1/3x 6?

Y = 1/3x? 6 ... slope here is 1/3. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will have a slope of - 3 (see how I flipped 1/3 and changed the sign)

y = mx + b

slope (m) = - 3

(-9,12) ... x = - 9 and y = 12

now we sub and find b, the y int

12 = - 3 (-9) + b

12 = 27 + b

12 - 27 = b

-15 = b

so ur perpendicular equation is : y = - 3x - 15