Question

The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this scenario is y = 170x – 4. Is her equation correct? Explain.

Answer 1

Answer:

No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.

Step-by-step explanation:

Answer 2

1. y=f(x)=170x-4 is a function with variable x representing a year.

2. Let's consider the difference between 2 consecutive years, say year 3 and year 4

f(3)=170*3-4
f(4)=170*4-4

we expect f(3)-f(4) to be 4 since after 4 years, the water will be 4 feet less than after 3 years.

check: f(3)-f(4)=(170*3-4)-(170*4-4)=170*3-4-170*4+4=170*3-170*4=170*(3-4)=170*(-1)=-170