Determine whether the following functions are linear or non-linear and explain how you know.
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Lesson 5 introduction to linear relationships; object lesson 6 more bilinear relationships; lesson 7 representations of additive relationships; lesson 8 translating to y=mx+b; finding slopes.
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Substitute the x values of the equation to find the values of y.
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In session 2, we used patterns and variables to describe relationships fashionable tables and fashionable situations like toothpicks and triangles.
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How to model a linear relationship between two quantities?
(8.EE.6) Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.
How to explore the slope of a linear relationship?
After exploring the rate of change of a linear relationship, students are introduced to the concept of slope and use the properties of dilations to show that the slope is the same between any two distinct points on a non- vertical line. Finally, students synthesize concepts learned and derive the equation of a line.
When do students shift to exploring linear relationships?
In eighth grade, a shift takes place as students move from proportional linear relationships, a special case of linear relationships, to the study of linear relationships in general. Students explore the growth rate of a linear relationship using patterns and contexts that exhibit linear growth.
What do you need to know about linear relations?
Students should come with an understanding of what a unit rate is and how to compute it. In addition they need to be able to recognize and represent proportional relationships from a story, graph, table, or equation. In addition they must identify the constant of proportionality or unit rate given different representations.
Last Update: Oct 2021
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Chapter 1: real Numbers ; chapter 2: exponents and knowledge base notation; chapter 3: proportional relationships; chapter 4: nonproportional relationships; chapter 5: authorship linear equations; chapter 6: functions; chapter 7: solving bilinear equations; chapter 8: solving systems of linear equations; chapter 9: transformations and congruenc.
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