Find the equation of the line that passes through the point left-parenthesis 1 comma 2 right-parenthesis and is perpendicular to the line negative startfraction 5 over 6 endfraction x plus startfraction 6 over 5 endfraction y equals negative 5

5/6x + 6/5y = -5
6/5y = -5/6x - 5...multiply by 30
36y = -25x - 150
y = -25/36x - 25/6the slope here is -25/36. A perpendicular line will have a negative reciprocal slope. All that means is flip the original slope and change the sign. So the perpendicular line will have a slope of 36/25.

y = mx + b
slope(m) = 36/25
(1,2)...x = 1 and y = 2
now we sub and find b, the y int
2 = 36/25(1) + b
2 = 36/25 + b
2 - 36/25 = b
50/25 - 36/25 = b
14/25 = b

so ur perpendicular equation is : y = 36/25x + 14/25