Write an equation for the line perpendicular to 9x + 8y = -75, through (-3, 6).

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Dear Student Thank you for using Chegg !! 9x + 8y = -75 Now writing this equation in slope intercept form we get 8y = -9x - 75 y = (-9/8)x -75/8 => Slope of given line is (-9/8) Now if two lines are perpendicular product of their slopes is -1 m1*m2 = -1 Slope of line perpendicular to given line is -1/(-9/8) Slope= 8/9 Hence equation of a line perpendicular to given line is y = (8/9)x + c Now given that this line passes through (-3,6) 6 = (8/9)(-3) + c 6+8/3 = c c = 26/3 Equation of new line is y = (8/9)x + 26/3 9y = 8x + 78 Solution

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