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Unit 5 – Linear Functions

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

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Unit 5 – Linear Functions

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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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