Let's analyze the given linear equation for the city's population:
[tex]\[ y = -80x + 3450 \][/tex]
where:
- [tex]\( y \)[/tex] represents the city's population.
- [tex]\( x \)[/tex] represents the number of years after 2000.
The equation consists of two main components:
1. Initial Population (Intercept): The constant term [tex]\( 3450 \)[/tex] indicates the initial population of the city in the year 2000 (when [tex]\( x = 0 \)[/tex]).
2. Rate of Change (Slope): The coefficient [tex]\( -80 \)[/tex] indicates the rate at which the population changes per year. Here, '-80' signifies a decrease in population.
### Step-by-Step Breakdown:
1. Initial Population in the Year 2000:
- At [tex]\( x = 0 \)[/tex], [tex]\( y = 3450 \)[/tex].
- Therefore, the population of the city in the year 2000 is 3450 people.
2. Population Change Per Year:
- The slope of [tex]\( -80 \)[/tex] implies that for each year after 2000, the population decreases by 80 people.
- Slope [tex]\( -80 \)[/tex] means that with every increment of one year (i.e., [tex]\( x \)[/tex] increases by 1), [tex]\( y \)[/tex] (population) decreases by 80.
### Description Based on the Equation:
The city's population decreases by 80 people each year starting from 3450 people in the year 2000.
This description encapsulates the essence of the given linear equation and succinctly explains how the population changes over time.
