Question 126141
The primary goal of this problem is to find the equation of a line. This is expressed as y = mx + b, where m is the slope of the line and b is the y-intercept (where the line crosses the y axis).

If we remove the "disguises" of dollars and number of items we are simply left with two x-coordinates and two y-coordinates as shown in the chart below:

x | y
_____
6 | 4
8 | 2

1. To find the slope of this line:
m = {{{(y2 - y1)/(x2 - x1)}}} = {{{(4 - 2)/(6 - 8)}}} = {{{2/-2}}} = -1 
Using y = mx + b:
      y = -1x + b

2. Substitute for x and y (plug in either of the two points - we'll use (6,4)):
      y = mx + b
      4 = -1(6) + b
3. Find the y-intercept by solving for b:
      4 = -6 + b
      b = 10
The equation is:
      y = -x + 10

Check:
Point (6,4)
      4 = -(6) + 10 
      4 = 4
Point (8,2)
      2 = -(8) + 10
      2 = 2