Question 1102492
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Find the equation of the line passing through the point (3, 7) and
perpendicular to the line 3y = 4 – 2x
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The given line  y = {{{(-2/3)*x}}} + {{{4/3}}} has the slope of {{{-2/3}}}.

Since the projected/requested line is perpendicular to the given line, it has the slope value opposite to reciprocal, i.e. {{{3/2}}}.

Hence, the projected/requested line has an equation of the form  y = {{{(3/2)*x + b}}}  with unknown coefficient "b".

To find "b", simply substitute the coordinates of the given point x= 3 and y= 7 respectively into this equation  y = {{{(3/2)*x + b}}}.  You will get

7 = {{{(3/2)*3 + b}}},   or  14 = 3*3 + 2b,

which implies  2b = 14 - 9 = 5  and  b = {{{5/2}}}.


Thus your final equation of the projected/requested straight line is 

y = {{{(3/2)*x + 5/2}}},  or  2y = 3x + 5.
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