Lesson plan

Derive the equation for a line intercepting the y-axis at the origin by graphing and 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: In a proportional relationship, the rate of change is the ratio of any non-zero y value to its associated x value, so a graph of the relationship can be created by drawing a line through the origin and a point x horizontal and y vertical units away, or by using a table of values. 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. In this task, students will read a verbal description for a real-world situation involving a 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.This lesson should be taught after students have learned to find slope, but before they learn to graph non-proportional linear relationships. Vocabulary: independent variable, dependent variable, initial value Special Materials: graph paper ruler