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Original line = 4x + 3y = 9
Point = (-2, 3)
1.- Find the slope of the oriinal line
4x + 3y = 9
3y = -4x + 9
y = -4/3 x + 9/3
Slope = -4/3
2.- Find the slope of the perpendicular line
Slope = 3/4
3.- Find the equation of the new line
y - y1 = m(x - x1)
y - 3 = 3/4(x + 2)
y - 3 = 3/4 x + 3(2)/4
y - 3 = 3/4 x + 6/4
y - 3 = 3/4 x + 3/2
y = 3/4x + 3/2 + 3
y = 3/4x + 9/2 This is the equation in the form slope intercept
3/4x - y = -9/2 This is the equation