Question

2 look ahead this table and graph represent the speed of a different blue whale over a period of 5 minutes. time (min) 0 1 2 3 4 5 distance (mi) 0 0.4 0.8 1.2 1.6 2 a. what is the unit rate for this proportional relationship? what does the unit rate mean in this situation? b. the point (2.5, 1) is also on the line. what is the vertical change between (2.5, 1) and (5, 2)? what is the horizontal change? c. the unit rate for a proportional relationship describes the rate of change between the variables. the rate of change is the quotient of the vertical change, or change in the y - variable, and the corresponding horizontal change, or change in the x - variable. on a graph, the rate of change is called the slope. use your answers to problem 2b to find the slope of the line between (2.5, 1) and (5, 2).

Explanation:

Step1: Find unit rate

Unit rate = $\frac{\text{Distance}}{\text{Time}}$. From the table, when time $t = 1$ min, distance $d=0.4$ mi. So unit rate = $\frac{0.4}{1}=0.4$ mi/min. It means the blue - whale travels 0.4 miles per minute.

Step2: Calculate vertical and horizontal change

For points $(x_1,y_1)=(2.5,1)$ and $(x_2,y_2)=(5,2)$, vertical change $\Delta y=y_2 - y_1=2 - 1 = 1$. Horizontal change $\Delta x=x_2 - x_1=5 - 2.5 = 2.5$.

Step3: Calculate slope

Slope $m=\frac{\Delta y}{\Delta x}$. Since $\Delta y = 1$ and $\Delta x = 2.5$, then $m=\frac{1}{2.5}=\frac{1\times2}{2.5\times2}=\frac{2}{5}=0.4$.

Answer:

a. Unit rate: 0.4 mi/min. It means the blue - whale travels 0.4 miles per minute.
b. Vertical change: 1, Horizontal change: 2.5.
c. Slope: 0.4