How do you write an equation of a line passing through (1,2), perpendicular to #2y+5 = 3x#?

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Answer 1 · 2016-08-29T22:36:53

#y = -2/3x +2 2/3#

Re-arrange the equation of the given line: #y = 3/2x-5/2#

The slope of this line is : # m_1 = 3/2#
The slope of a line perpendicular to this line is:

#m_2 = -2/3#

We have the slope and a point, (1,2) which is #(x_1,y_1)#

Substitute into the formula:
#y-y_1 =m(x-x_1)#

#y-2 = -2/3(x-1)#

#y= -2/3x +2/3+2#

The equation is:
#y = -2/3x +2 2/3#