We want to see which of the listed situations can be modeled with linear equations. We will see that the situations that are linear are:
- "He sells 5 propane stoves each day for 4 consecutive days"
- "Cooper's profit decreases by $125 each day for 5 days"
- "Cooper sells 2 fewer fishing poles each day for 1 week".
Finding situations that are linear
First, a linear equation shows a dependence of two variables as:
y = a*x + b
Where y and x are the variables, a is the slope and b is the y-intercept.
Let's see which situations can be written in this form.
"He sells 5 propane stoves each day for 4 consecutive days."
If we define y = number of propane stoves sold and x = number of days, then we can write this as:
y = 5*x
Where x goes from 0 to 4, so this can be represented with a linear equation.
"Cooper's profit decreases by $125 each day for 5 days."
Similar to before, we have a fixed change per day, so this again can be modeled with a linear equation.
"Cooper's profit doubles each month for 3 consecutive months."
This can not be modeled with a linear equation, the problem here is that the change is not fixed.
Because the profit is doubled, the change will depend on the value of the profit (so the double of 4 is not the same as the double of 5, just to give an example). Thus, this can not be modeled with a linear equation, this actually needs an exponential equation.
"Cooper sells 2 fewer fishing poles each day for 1 week."
Similar to the first and second case, each day he has 2 fewer fishing poles, a fixed number per day, thus, this can be modeled with a linear equation.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4025726
