Alternatives to Slope and Intercept
In this lesson, the focus is on breaking away from the habit of using terms like slope and intercept when discussing linear models. Instead, the parameters in a linear model should be given meaning based on the context of the specific relationship being modeled. This requires a deeper understanding of functional notation and an ability to interpret the parameters in real-world situations. By using more descriptive and accurate language, such as referring to the rate or coefficient in the linear model, a clearer understanding of the relationship can be achieved.
Know what the two parameters in a linear model/function mean in the context of real relationships. Recognize the vocabulary used for these parameters depending on the context constant rate / slope / coefficient and initial value / vertical intercept / constant.
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- Problem Set - Problem set from this lesson.
- Problem Set Solutions - Solutions to the problem set from this lesson.
- Notes - Notes from this lesson.
- What are some other terms / names for slope and y-intercept?
- What do m and b mean in y = mx + b?
- What are the parameters, input, and output in the function x = y(f) = af + z?
- What do rate and coefficient mean in a linear function?
- What do initial value, vertical intercept, and constant mean in a linear function?
- What is a relationship with a constant rate of change?
- What is an output axis intercept?
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Staff Review
This lesson tries to move you away from a line looking like y = mx + b. Using full functional notation, a function can use any letters to represent the input and output as well as the parameters. Therefore, you will learn more descriptive names for the slope and y-intercept in a linear model. The problem set and solutions will help this make more sense to you.
