Question 117230
find the equation of the line perpendicular to {{{ y = -2/3x - 4 }}} and passes through (-2,5)
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If the line is perpendicular,its slope will be the negative reciprocal of the original line's slope, m.

{{{y=-2x/3-4}}}
is in the form of equation of line----y=mx+b
So, the original line has a slop of -2/3

The negative reciprocal of -2/3 is 3/2.

So, the new line has slope,m=3/2

Since you are given the point which the new line goes through use the point-slope form to find its equation:

(x1,y1)=(-2,5)

(y-y1)=m(x-x1)

(y-5) = 3/2(x-(-2))

{{{y-5=3/2(x+2)}}}

{{{y-5=3x/2 +3}}}

Put equation into the standard form,y=mx+b.

y=3x/2+3 +5

{{{y=3x/2 + 8}}}

Hope that helps.

Regards,
misscrt