The table includes the cost of ordering different numbers of fence sections. number of sections (x) cost in dollars (y) 10 409 50 1,889 125 4,664 if the cost is a function depending on the number of sections, how much will 200 sections cost? $7,400 $7,439 $7,556 $7,837

It will cost $7439.

We first find the rate of change between consecutive points.  Between the first two,
m = (1889-409)/(50-10) = 1480/40 = 37

Between the second two points,
m = (4664-1889)/(125-50) = 2775/75 = 37

Since the rate of change is the same between points, this is a linear situation.

Writing the equation of the line in point-slope form, we have
y - 409 = 37(x - 10)

Using 200 as x,
y - 409 = 37(200 - 10)
y - 409 = 37(190)
y - 409 = 7030

Adding 409 to both sides,
y = 7030+409 = 7439