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Linear functions

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This resource from Duy Tan University, presented by teacher Nguyen Thi Le Nhung, covers the fundamentals of linear functions, including their equations and slopes. It illustrates how to express total cost based on production units, demonstrating practical applications through real-world examples. The material includes a detailed explanation of the constant rate of change in linear functions and how to graph them effectively. Students will learn to determine the relationship between variables and find the y-intercept, as well as understand market price changes over time.

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Linear functions

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  1. DUY TAN UNIVERSITY Teacher: Nguyen Thi Le Nhung Linear functions 3. The equation of a line 1. Linear functions 2. Slope of a line

  2. DUY TAN UNIVERSITY Linear functions Example 1: A manufacturer’s total cost consits of a fixed over head of $200 plus production costs of $50 per unit. Express the total cost as a function of the number of units produced and draw the graph. Solution: Let x denote the number of units produced and C(x) the corresponding total cost. Then, Toatal cost = (cost per unit)(number of units) + overhead Hence,

  3. DUY TAN UNIVERSITY

  4. DUY TAN UNIVERSITY Linear functions 1. Linear functions A linear function is a function that changes at a constant rate with respect to its independent variable. The graph of a linear function is a straight line. The equation of a linear function can be written in the form where m and b are constants.

  5. DUY TAN UNIVERSITY Linear functions 2. Slope of a line The slope of the nonvertical line passing through the points (x1,y1) and (x2,y2) is given by the formula 3. The equation of a line The equation is an the equation of the line that passes through the point (x0 , y0) and that has slope equal to m .

  6. DUY TAN UNIVERSITY Linear functions Practical applications Example 1 Since the beginning of the year, the price of a certain commodity has been rising at a constant rate. By June first, the price had reached $12 per unit and by November first, the price had reached $14.5 per unit. Express the price of the commodity as a function of time and determine the price at the beginning of the year.

  7. DUY TAN UNIVERSITY Linear functions Solution: Let x denote the number of months that have elapsed since the first of the year and y the price of a unit. Since y changes at a constant rate with respect to x, the function relating y to x must be linear, and its graph is a straight line. The fact implies that the line pass through two points ( 5, 12) and (10, 14.5). Hence, the slope The equation of the line: with To get The y intercept is (0, 7.5), which implies that the price of commodity at beginning of the year was $7.5 per unit.

  8. DUY TAN UNIVERSITY Thank you for listening!

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