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

2. Example 1: Linear functions DUY TAN UNIVERSITY 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. Let x denote the number of units produced and C(x) the corresponding total cost. Then, Solution: Toatal cost = (cost per unit)(number of units) + overhead Hence,

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4. 1. Linear functions Linear functions DUY TAN UNIVERSITY 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. The slope of the nonvertical line passing through the points (x 1, y 1 ) and (x 2, y 2 ) is given by the formula 2. Slope of a line DUY TAN UNIVERSITY The equation 3. The equation of a line is an the equation of the line that passes through the point (x 0, y 0 ) and that has slope equal to m. Linear functions

6. DUY TAN UNIVERSITY 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. Linear functions

7. DUY TAN UNIVERSITY Let x denote the number of months that have elapsed since the first of the year and y the price of a unit. Solution: 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. Linear functions

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