Question

a-27. at an aunts wedding, nicolas collected data about an ice sculpture that was about to completely melt. a graph of his data is shown below. a. calculate the equation of a line of best fit. b. based on your equation, how tall was the ice sculpture one hour before nicolas started measuring?

Explanation:

Step1: Find the slope $m$

Choose two points, say $(0, 10)$ and $(4,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{0 - 10}{4-0}=\frac{- 10}{4}=-\frac{5}{2}$.

Step2: Find the y - intercept $b$

The line is in the form $y = mx + b$. When $x = 0$, from the graph $y=10$, so $b = 10$. The equation of the line of best - fit is $y=-\frac{5}{2}x + 10$.

Step3: Solve part b

The starting time of measurement is $x = 0$. One hour before is $x=-1$. Substitute $x=-1$ into $y=-\frac{5}{2}x + 10$. Then $y=-\frac{5}{2}\times(-1)+10=\frac{5}{2}+10=\frac{5 + 20}{2}=\frac{25}{2}=12.5$.

Answer:

a. $y =-\frac{5}{2}x + 10$
b. $12.5$ inches