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

200 sections will cost $7439.

We first see if the rate of change, the slope, is the same between data points.  If it is, the function will be linear.  We use the formula

m = (y₂ - y₁)/(x₂ - x₁)

For the first two data points, we have

m = (1889-409)/(50-10) = 1480/40 = 37

For the second two data points, we have

m = (4664-1889)/(125-50) = 2775/75 = 37

Now that we know the slope is the same, we can write the equation:
y - y₁ = m(x - x₁) 
y - 409 = 37(x - 10)
y - 409 = 37x - 370

Add 409 to both sides: 
y = 37x + 39

Using 200 as x,
y = 37(200) + 39 = 7439