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)?

Perpendicular means that the slope is exact opposite
so if the slope is 2/3 then on the perpendicular line it'll be 3/2
y = 3/2x + b
to solve for b, plug in the given coordinate
2 = 3/2 (4) + b
2 = 6 + b
subtract 6 from both sides
-4 = b

the equation for the line that passes perpendicular to y = 2/3x + 5 is:
y = 3/2x - 4

Hope this helps :)

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