Lesson plan

Derive the equation for a line intercepting the y-axis at a point other than the origin by analyzing a real-world situation

teaches Common Core State Standards CCSS.Math.Content.8.EE.B.6 http://corestandards.org/Math/Content/8/EE/B/6

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Big Ideas: The equation for a line can be written in the form y = mx or y = mx + b, where m represents the rate of change for the independent variable x, and b (called the initial value) represents the value of the dependent variable y when the value of x is zero. A line has a well-defined slope; that is, the ratio between the rise and run for any two points on the line is always the same. This is because any two right triangles with hypotenuses on the line must necessarily be similar. In this task, students will read a verbal description for a real-world situation involving a non-proportional relationship, define the independent and dependent variables, create a table of values, and graph the line to represent the situation. Then they will formulate a function rule illustrating the relationship between the independent and dependent variables, and use that information to write an equation for the line. They will also contrast proportional and non-proportional relationships by identifying differences in observed patterns. This lesson should follow writing the equation for proportional relationships; it should precede the introduction to functions. Vocabulary: independent variable, dependent variable, slope (rate of change), initial value Special Materials: graph paper ruler