Question

interpolating data
heather is training for a long - distance run. her data points listed below represent the days of practice, x, and the number of miles run, y.
(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)
use the equation to interpolate the value and estimate the distance that she could have run on day 3. round to the nearest tenth of a mile.
day 3 ≈ miles

Explanation:

Step1: Identify adjacent points

Day 3 is between (2,4.2) and (4,5.6).

Step2: Apply linear interpolation formula

$y = 4.2 + (3-2)\cdot\frac{5.6-4.2}{4-2}$

Step3: Calculate the value

$y = 4.2 + 1\cdot\frac{1.4}{2} = 4.2 + 0.7 = 4.9$

Answer:

4.9