Question

grade / accelerated
name
unit 10
date
lesson 4 practice
period
the community of siesta key, florida has the fastest shrinking population in the state. in
2010 the population of siesta key was 6,568. then in 2019, the population was 5,570. it
was determined that in 2021, the linear pattern continued.

1. calculate the rate of change of the siesta key population.
2. determine whether the rate of change represents an increase or decrease in the

population of siesta key.

1. based on the answers to the previous questions, what is the slope of this linear

relationship?

1. complete the statement to interpret the slope as the rate of change for this

context.
in this context, the slope means that the population of siesta key
◦ increases
◦ decreases
by
◦ 5,570
◦ 998
◦ 110
◦ year
◦ people
per
◦ year.
◦ people
the graph shows how the length of gabbys book report depends on the number of hours
she spends writing.

1. find the slope of the line.
2. interpret the slope for this context.

Explanation:

Step1: Calculate the rate of change

The formula for the rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(x_1 = 2010,y_1=6568,x_2 = 2019,y_2 = 5570\). Then \(m=\frac{5570 - 6568}{2019 - 2010}=\frac{-998}{9}\approx - 110.89\approx - 110\) (rounded to the nearest whole number).

Step2: Determine increase or decrease

Since the rate of change \(m=-110\lt0\), the population is decreasing.

Step3: Identify the slope

The slope of the linear relationship is the rate of change. So the slope \(m=-110\).

Step4: Interpret the slope

In the context of population change, the slope means that the population of Siesta Key decreases by 110 people per year.

For the graph of Gabby's book - report:

Step5: Find the slope (assuming two points \((0,0)\) and \((1,2)\) (since the line passes through the origin and if \(x = 1,y=2\))

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,2)\), we get \(m=\frac{2 - 0}{1 - 0}=2\).

Step6: Interpret the slope

In the context of Gabby's book - report, the slope means that the length of the book report (in pages) increases by 2 pages per hour.

Answer:

1. The rate of change is \(-110\).
2. The population is decreasing.
3. The slope is \(-110\).
4. In this context, the slope means that the population of Siesta Key decreases by \(110\) people per year.
5. The slope of the line (for Gabby's book - report) is \(2\).
6. In this context, the slope means that the length of Gabby's book report increases by \(2\) pages per hour.