write slope intercept form of the equation of the line described through 5,3 parallel to y=2/3x-2

Question

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Answer 1

The line you have (2/3)x-2 has a slope of 2/3, as will the line you want.  Its equation will be y=(2/3)x+b, where the b is chosen so that the line passes through (5,3).  3=(2/3)5+b or 3=10/3+b or b=-1/3.  The equation is y=(2/3)x-1/3