Скачать или смотреть Proportional Linear Relationships & Slope | 8.EE.B.5 💗

In this video lesson we will learn about proportional linear relationships and slope. We will begin by understanding that proportional linear relationships are special linear relationships whose graph is a line passing through the origin. We will apply our understanding of ratios, rates, and unit rates to slope. We will understand that the ratio of any ordered pair, y to x, of a proportional relationship represents the constant of proportionality. The constant of proportionality is a special slope when the line represents a proportional relationship. We will learn that slope is a ratio of the change in y to the change in x. We will learn how to find slope of a graph. We will learn that when slope or constant of proportionality is in simplest form, or has a denominator of 1, that it represents the unit rate. We will learn how to represent and interpret a proportional linear relationship using words, a table, an equation, and a graph. We will learn how to interpret slope. We will compare two different proportional linear relationships represented in two different ways. Student practice is embedded in the lesson with modeled exemplar solutions.

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00:00 Introduction
00:46 Vocabulary: linear and proportional relationships
02:34 Four Ways to Represent a Proportional Relationship
06:33 Solutions of an Equation
09:47 Rate of Change & Slope
11:14 Constant of Proportionality
12:51 Unit Rate & Slope
14:57 Finding Slope
16:52 Interpret Slope
18:27 How to Graph the Equation of a Line
22:28 Student Practice #1 - Compare Linear Relationships
25:24 Student Practice #2

Common Core Math Standards
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Use functions to model relationships between quantities.
8.F.B.4 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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.