- Describe a real-world situation in which the relationship between the independent and dependent variable is linear.
- In your description, indicate what each coordinate represents in terms of the situation and what conclusions can be drawn in terms of the graph’s behavior.
- Your postings should also:
- Be well developed by providing clear answers with evidence of critical thinking.
- Add greater depth to the discussion by introducing new ideas.
Let the independent variable be the number of years you have worked at a company and the dependent variable your yearly wage. Further, suppose that each year you receive a raise of $1500.
The relationship between years at the company and your yearly wage will be linear. If the starting wage was $30,000, then the relationship can be described or modeled by the function w=1500Y+30000 where W is the wage and Y is the number of years.
A given coordinate, say (3,34,500) represents that you have worked 3 full years for the company, and this year your wages will be $34,500. In the model, the 1500 represents the yearly increase in earnings, while the 30000 represents the initial value (i.e. when you are first hired.)
Note that for this example, the domain (accepted inputs for the independent variable) are non-negative integers.
If you would prefer a continuous model (i.e. a model that accepts any real number as an input) consider the following:
Let the independent variable be rainfall in inches, and the dependent variable be the depth of a certain lake. We suppose that the area drained by the lake and the shape of the lake are such that as each inch of rain falls, the lake's depth increases by 1/2 inch.
Then the model is D=1/2R+960. Here 960 inches is the initial depth of the lake, R is the amount of rainfall in inches, and D the depth of the lake in inches.
Another example (that I have also gotten in school in the past and have discusses in a previous post) is the way to calculate the cost of renting a car. There may be an upfront fee for renting the car for a day, but then there might be a variable fee that depends on the number of miles driven. However, this may be a simplification of the car rental process in order to fit the linear example.
This car cost example can be expanded to be "more real" while still fitting the linear relationship. Let's assume that you buy a car in full - no monthly payments for you, the car is yours. Even though when you actually drive and use gas, you fill up on gas and therefore spend money in spurts, let's say that you averaged this money out and know the cost per mile. Then, this cost per mile would be your variable cost. In this example, the number of miles would be the independent variable and the cost would be the dependent variable. Graphing cost on the y-axis and number of miles on the x-axis, your (signficant) upfront cost of buying the car would be the y-intercept.