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In the first module, students will learn a process they can use to create an equation to represent a linear relationship. Students will identify the proportion that represents the rate of change, then they cross multiply and isolate to write the equation in the form px + q = r, and finally, they add (a positive or negative) to adjust for the initial, or starting, value in the problem situation.
Students will then figure out the function hidden inside each of several linear function machines by entering inputs and observing the outputs generated by the machine and recorded in an x-y (input-output) table. Functions involve positive, negative, and 0 slopes and positive and negative y-intercepts. Students determine the rate of change, or slope, whether the linear function is increasing, decreasing, or neither, and the value of the function at x = 0 (the y-intercept).
Finally, students write and evaluate linear functions, given a small variety of different problem situations. Students use function notation to evaluate functions at given inputs, and they determine ordered pair solutions for functions. Students write linear functions for situations by identifying whether the function is increasing, decreasing, or neither, and determining the y-intercept.
Module 3 Video
This video introduces the basics of linear functions. Ask students to tell whether the first function, f(x) = 2x + 3, is increasing, decreasing, or neither, and why. Do the same for the skier function and for the plane function at the end. Have students compare the graphical representation of the skier’s function with the table representation for the plane’s function.