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The equation of a line is y=2/3x+5. What is an equation of the line that is perpendicular to the given line and that passes through the point (4,2)?

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seizetheday
The gradient of this line is 2/3 so the gradient of the perpendicular line is -3/2 (the two perpendicular gradients must multiply to get -1).

Using the formula y - y1 = m (x - x1):

y-2=-1.5(x+4)

This can be rearranged to:

2y-4=-3x-6
2y+3x=-2