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Introduction to Linear Functions: Understanding the Basics of Linearity and Graphing

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This unit introduces the concept of linear functions, emphasizing the degree of x and its implications. Learn to identify linear equations versus nonlinear equations by examining the degree, where a degree of 1 indicates a linear function. Explore the standard form of a linear equation (Ax + By = C) and discover how to graph lines using intercepts. Use real examples to solidify understanding and complete journal prompts to reflect on prior knowledge, new learning, and lingering questions. This foundational knowledge is essential for advancing in algebra.

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Introduction to Linear Functions: Understanding the Basics of Linearity and Graphing

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  1. Unit 5 – Linear Functions Topic: Introduction To Linear Functions

  2. What is a linear function? • Degree of x is always 1. • “Degree” refers to the largest exponent of x. • Ex. Which equation represents a linear function? Degree (largest exponent) of xfor f(x) is 1. Degree of x for g(x) is 2. Therefore, f(x) is linear, g(x) is not.

  3. Change in both x & y is always constant. • Ex. Which set of ordered pairs represents a linear function? • REMINDER: Change in x doesn’t have to equal change in y; each change just needs to be constant. {(1, 25), (2, 16), (3, 9), (4, 4), (5, 1)} Change in x is constant (+1). Change in y is not. Nonlinear function. {(1, -5), (2, -3), (3, -1), (4, 1), (5, 3)} Change in x is constant (+1). Change in y is constant (+2). Linear function. What is a linear function?

  4. Graph forms a line (I assume you know what a line looks like). • JOURNAL ENTRY • TITLE: Lines & Functions • Are all lines also functions? If so, explain why. If not, give an example of a line that is not a function. What is a linear function?

  5. Standard Form of a Linear Equation • Ax + By = C • Ais an non-negative integer. • B, C are integers. • A & B cannot both be 0. • Examples:

  6. Graphing Linear Equations in Standard Form • To graph a line, you need at least two points. • In standard form, the easiest points to identify are the x- and y-intercepts. • For x-intercept, y = 0. • For y-intercept, x = 0.

  7. Graphing Linear Equations in Standard Form • Graph the function 3x – 2y = 12 • x-intercept: set y = 0, and solve for x • Plot the point (4, 0).

  8. Graphing Linear Equations in Standard Form • Graph the function 3x – 2y = 12 • y-intercept: set x = 0, and solve for y • Plot the point (0, -6). • Connect the points with a line.

  9. TITLE: Checking My Understanding: Intro. To Linear Functions • Review your notes from this presentation & create and complete the following subheadings in your journal: • “Things I already knew:” Identify any information with which you were already familiar. • “New things I learned:” Identify any new information that you now understand. • “Questions I still have:” What do you still want to know or do not fully understand? JOURNAL ENTRY

  10. Handout will be given in class • Due 11/4 Homework

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