Hi

Using the standard slope-intercept form for an equation of a line y = mx + b 

 where m is the slope and b the y-intercept.  



Line thru (4,2) where m= -2/3

 y = (-2/3)x + b   |using ordered pair Pt(4,2) to solve for b

 2 = -8/3 + b

 14/3 = b     

y = (-2/3)x + 14/3  |standard form: 2x + 3y = 14



Thru (9,2)and 'perpendicular' to 3x+2y=31 OR y = (-3/2)x +31/2

slope of line perpendicular to it would be 2/3.  (negative reciprocal)

 y = (2/3)x + b    |using ordered pair Pt(9,2) to solve for b

 2 = 6 + b

 -4 = b

 y = (2/3)x -4  

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