Question

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 = 4.9 miles

Explanation:

Step1: Find the equation of the line using two - point form

The two - point form of a line is $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. Let's take two points, say $(2,4.2)$ and $(4,5.6)$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{5.6 - 4.2}{4 - 2}=\frac{1.4}{2}=0.7$. Using the point $(2,4.2)$, the equation of the line is $y-4.2 = 0.7(x - 2)$.

Step2: Simplify the equation

Expand the right - hand side: $y-4.2=0.7x - 1.4$. Then $y=0.7x+2.8$.

Step3: Substitute $x = 3$ into the equation

When $x = 3$, $y=0.7\times3 + 2.8=2.1+2.8 = 4.9$.

Answer:

$4.9$