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Linear functions

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

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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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