Using the given points (4, 220) and (7, 340), we can calculate the slope:
slope = (change in y) / (change in x)
slope = (340-220) / (7-4)
slope = 120 / 3
slope = 40
Now we can use the point-slope form to find the equation:
y - y1 = m(x - x1)
y - 220 = 40(x - 4)
y - 220 = 40x - 160
y = 40x + 60
Therefore, the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost is y = 40x + 60, where y represents the total cost and x represents the number of cubic yards of soil ordered.