Question

interpolating from data
enter values for x and y in the table to plot points in the graph.
these data points represent the relationship between
the size of a house (in 1000 square feet) and its price
(in $100,000).
(1.2, 1.7), (1.4, 2), (1.5, 2.2), (1.6, 2.3), (1.8, 2.5), (1.9,
2.6), (2.1, 2.9), (2.2, 2.8), (2.4, 3.4), (2.7, 3.1)
use the trend line to predict the cost of a 2,000 - square -
foot house.
$200,000
x $233,000
$267,000
$300,000

Explanation:

Step1: Analyze the data relationship

The \(x\) - values represent the size of the house in \(1000\) square - feet and \(y\) - values represent the price in \(\$100,000\). A \(2000\) - square - foot house has \(x = 2\) (since \(x\) is in units of \(1000\) square - feet).

Step2: Use linear interpolation or trend - line approximation

Looking at the data points around \(x = 2\). The data points \((1.9,2.6)\) and \((2.1,2.9)\). The general formula for linear interpolation between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(y=y_1+\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)\). Here \(x_1 = 1.9,y_1=2.6,x_2 = 2.1,y_2 = 2.9,x = 2\).

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Since \(y\) is in units of \(\$100,000\), the price is \(y\times100000\)

Answer:

\(\$275000\)