Let `x` be the number of adults that buy tickets and `y` the number of students that buy tickets. The problem says that each ticket for an adult costs $5 and each ticket for a student costs $3, and that the total sum wanted to be raised is $450. The corresponding equation to show this is

`5*x +3*y =450`

This is the standard form of equation of a line, in 2D space. If we want to place it in slope-intercept form we need to separate the variables:

`3y =-5x +450` or equivalent

`y = -5/3*x +150`

Thus the slope of the line representing the equation is `m=-5/3` and the `y` intercept (`x=0` ) is `y0 =150` . The graph is below attached. Since negative values of `x` and `y` (number of persons) does not have physical significance, the graph is restricted only to the first quadrant.

From the graph, we se that two pairs `(x,y)` which satisfies the above equation are `(42,80)` and `(60,50)` .

**Therefore the sum can be raised selling 42 tickets for adults and 80 tickets for students or alternately selling 60 tickets for adults and 50 tickets for students.**