 # Relationships between Two Numerical Variables

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Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn about relationships between two numerical variables: Linear, Quadratic, Exponential

### New York State Common Core Math Algebra I, Module 2, Lesson 12, Lesson 13

Worksheets for Algebra I, Module 2, Lesson 12 (pdf)
Worksheets for Algebra I, Module 2, Lesson 13 (pdf)

Lesson 12 Student Outcomes

Students distinguish between scatter plots that display a relationship that can be reasonably modeled by a linear equation and those that should be modeled by a nonlinear equation.

Lesson 12 Summary

• A scatter plot can be used to investigate whether or not there is a relationship between two numerical variables.
• A relationship between two numerical variables can be described as a linear or nonlinear relationship.

When a straight line provides a reasonable summary of the relationship between two numerical variables, we say that the two variables are linearly related or that there is a linear relationship between the two variables.

Exit Ticket

1. You are traveling around the United States with friends. After spending a day in a town that is 2000 feet above sea level, you plan to spend the next several days in a town that is 5000 feet above sea level. Is this town likely to have more or fewer clear days per year than the town that is 2000 feet above sea-level? Explain your answer.
2. You plan to buy a bike helmet. Based on data presented in this lesson, will buying the most expensive bike helmet give you a helmet with the highest quality rating? Explain your answer.

Lesson 13

Not all relationships between two numerical variables are linear. There are many situations where the pattern in the scatter plot would best be described by a curve. Two types of functions often used in modeling nonlinear relationships are quadratic and exponential functions.

Lesson 13 Student Outcomes

Students distinguish between scatter plots that display a relationship that can be reasonably modeled by a linear equation and those that should be modeled by a nonlinear equation.

Students use an equation given as a model for a nonlinear relationship to answer questions based on an understanding of the specific equation and the context of the data.

Lesson 13 Summary
• A scatter plot can be used to investigate whether or not there is a relationship between two numerical variables.
• Linear, quadratic, and exponential functions are common models that can be used to describe the relationship between variables.
• Models can be used to answer questions about how two variables are related.

Exit Ticket

1. Here is the scatter plot of age (in years) and finish time (in minutes) of the NY City Marathon that you first saw in an example. What type of model (linear, quadratic or exponential) would best describe the relationship between age and finish time? Explain your reasoning.

2. Here is the scatter plot of frying time (in seconds) and moisture content (as a percentage) you first saw in Lesson 12. What type of model (linear, quadratic or exponential) would best describe the relationship between frying time and moisture content? Explain your reasoning.

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