Find the equation that passes through (-5,1) and is perpendicular to the line 2x+3y=12

First rewrite 2x + 3y = 12 as  y = -(2/3)x + 4.  The slope of this line is -(2/3), so the slope of a line perpendicular to this must be +(3/2).  

This means the equation of the perpendicular line is of the form y = (3/2)x + k  where k is a constant.

We can find the value of k because we know the line must pass through the point (-5,1).  That is:

1 = (3/2)*(-5) + k

k = 1 + 15/2

k = 17/2

Hence the line passing through (-5, 1) is y = (3/2)x + 17/2

or, by multiplying through by 2, we could rewrite this as 2y = 3x + 17

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