heather is training for a long - distance run. her data points listed below represent the days of practice…

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

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

Answer

Explanation:

Step1: Find the slope

We use two - point formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(1,2.5)$ and $(2,4.2)$. Then $m=\frac{4.2 - 2.5}{2 - 1}=\frac{1.7}{1}=1.7$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert it to slope - intercept form $y=mx + b$. Using the point $(1,2.5)$ and $m = 1.7$, we have $y-2.5=1.7(x - 1)$. Expanding gives $y-2.5=1.7x-1.7$. Then $y=1.7x+0.8$.

Step3: Interpolate for $x = 3$

Substitute $x = 3$ into the equation $y=1.7x + 0.8$. So $y=1.7\times3+0.8=5.1 + 0.8=5.9$.

Answer:

5.9