Question

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)?

Answer 1

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 :)