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.
8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
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Lesson 1: Modeling Linear Relationships (P)
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Lesson 2: Interpreting Rate of Change and Initial Value (P) Lesson 3: Representations of a Line (P) Lessons 4–5: Increasing and Decreasing Functions (P, P)
Related Topics: More Lesson Plans for Grade 8 Common Core Math In Topic A, students build on their study of functions by recognizing a linear relationship between two variables (8.F.B.4). Students use the context of a problem to construct a function to model a linear relationship (8.F.B.4). In Lesson 1, students are given a verbal description of a linear relationship between two variables, and then must describe a linear model. Students graph linear functions using a table of values and by plotting points. They recognize a linear function given in terms of the slope and initial value or intercept. In Lesson 2, students interpret the rate of change and the -intercept, or initial value, in the context of the problem. They interpret the sign of the rate of change as indicating that a linear function is increasing or decreasing (8.F.B.5) and as indicating the steepness of a line. In Lesson 3, students graph the line of a given linear function. They express the equation of a linear function as or an equivalent form when given the initial value and slope. In Lessons 4 and 5, students describe and interpret a linear function given two points or its graph. 1
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.
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