Question

interactive practice: graph proportional relationships and define slope
dr. castillo analyzes the carbon absorption in kelp forests with and without otters. she makes a
graph to compare the carbon absorbed in each type of kelp forest, in kilotons per day.
what is the slope of the line?
what is the slope of the line?
without otters: 14
with otters: 20
what do the slopes mean in this situation?
kelp forests without otters absorb carbon dioxide at a rate of?
kelp forests with otters absorb carbon dioxide at a rate of?

Explanation:

Step1: Understand the meaning of slope in a proportional relationship

In a proportional relationship \(y = mx\) (where \(y\) is the dependent variable, \(x\) is the independent variable, and \(m\) is the slope), the slope \(m\) represents the rate of change of \(y\) with respect to \(x\). Here, \(y\) is the amount of carbon absorbed (in kilotons) and \(x\) is the number of days.

Step2: Interpret the slopes for each case

• For the case without otters, the slope \(m = 14\). This means that for each additional day, the kelp forest without otters absorbs \(14\) kilotons of carbon. So, the rate of carbon - dioxide absorption for kelp forests without otters is \(14\) kilotons per day.
• For the case with otters, the slope \(m = 20\). This means that for each additional day, the kelp forest with otters absorbs \(20\) kilotons of carbon. So, the rate of carbon - dioxide absorption for kelp forests with otters is \(20\) kilotons per day.

Answer:

Kelp forests without otters absorb carbon dioxide at a rate of \(14\) kilotons per day. Kelp forests with otters absorb carbon dioxide at a rate of \(20\) kilotons per day.