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write an equation for the line that is perpendicular to the given line and that passes through the given point y=-1/3x+2;(4,2)

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The slopes of two perpendicular lines, when multiplied, have a product of -1.  Therefore, given the eq of the line with a slope of -1/3, we can conclude that the perpendicular line will have a slope of 3.

so to start, our equation of interest is y=3x + b, where b is unknown. 

Since we know that it passes through the point (4,2) we can plug the values of x and y into this equation to solve for b.  2 = 3*4 + b

2=12 + b

-10 = b  

This gives the entire equation we are after:  y=3x-10.