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)

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.

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