Question

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

Answer 1

Your answer will be B  :
$7,439

Answer 2

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