How do you write an equation of a line through (3,3) and parallel to y= 2/3x -1?

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Answer 1 · 2017-04-04T05:54:16

#y=2/3x+1#

Our reference line is: #y=2/3x-1#

Hence the slope of the reference line is: #2/3#

Any straight line parallel to the reference line will have a slope of #2/3#

We are asked to find the equation of the line parallel to the reference line passing through the point #(3,3)#.

The equation of a straight line passing through point #(x_1, y_1)# is:

#(y-y_1) =m(x - x_1)# Where #m# is the slope of the line.

Hence the equation of our required line will be:

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

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

#3y-9 = 2x-6#

#3y= 2x+3#

#y = 2/3x+1#