Question

Which statement is true based on the model Y = -0.5X + 26, where Y represents the amount of shoreline in feet X decades after 1950?

Option 1: The shoreline is increasing by 0.5 feet per decade.
Option 2: The shoreline is decreasing by 0.5 feet per decade.
Option 3: The shoreline remains constant at 26 feet.
Option 4: The shoreline is decreasing by 26 feet per decade.

Answer 1

The correct statement based on the model Y = -0.5X + 26 is that the shoreline is decreasing by 0.5 feet per decade, indicating progressive shoreline erosion over time.

Step-by-step explanation:

The statement that is true based on the model Y = -0.5X + 26 is Option 2: The shoreline is decreasing by 0.5 feet per decade. In this linear equation, Y represents the amount of shoreline in feet X decades after 1950.

The negative coefficient of X (-0.5) indicates that for each decade that passes, the shoreline decreases by 0.5 feet. The number 26 represents the y-intercept, which is the initial value of the shoreline in 1950.

Therefore, Option 3 is incorrect as the shoreline does not remain constant at 26 feet; it decreases over time. Option 1 is incorrect because the shoreline is decreasing, not increasing. Option 4 is also incorrect, as the rate of decrease is 0.5 feet per decade, not 26 feet.