Solution: As given line y =3x-5 meet x-axis at the point M.
On x axis y coordinate is zero.
Put y =0 in above equation, we get →x = 5/3
∴ Coordinate of M is (5/3,0).
As, also given , line 3y+2x=2 meets y-axis at point N.
On y axis , x coordinate is zero.
Substituting , x=0 in above equation, gives y =2/3.
Coordinate of point N is (0,2/3).
Equation of line passing through two points (a,b) and (p,q) is given by
→ 
Or as X intercept = 5/3, and Y intercept = 2/3
Equation of line in intercept form is →
, where a and b is X intercept and y intercept respectively.
So, line passing through (5/3,0) and (0,2/3) is given by
→ 
→
→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]
→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.