Question 405575
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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