The line 5x - 3y = 9 converts to slope intercept form as y = 5/3 x-3. When x = 30, it has the value y = 5/3(30) - 3 = 50 - 3 = 47. SO it has the point (30,47).
This line has a slope of 5/3. The line perpendicular to it will have the negative reciprocal slope -3/5. Using this slope and the point (30,47), we write the ine in point slope form: