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Unformatted text preview: Section 3.3 Equations of Lines 283 Version: Fall 2007 3.3 Exercises In Exercises 1 6 , perform each of the following tasks for the given linear func tion. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler. ii. Identify the slope and yintercept of the graph of the given linear function. iii. Use the slope and yintercept to draw the graph of the given linear function on your coordinate system. Label the yintercept with its coordinate and the graph with its equation. 1. f ( x ) = 2 x + 1 2. f ( x ) = − 2 x + 3 3. f ( x ) = 3 − x 4. f ( x ) = 2 − 3 x 5. f ( x ) = − 3 4 x + 3 6. f ( x ) = 2 3 x − 2 In Exercises 7 12 , perform each of the following tasks. i. Make a copy of the given graph on a sheet of graph paper. ii. Label the yintercept with its coor dinates, then draw a right triangle and label the sides to help identify the slope. iii. Label the line with its equation. Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 7. x y 5 5 8. x y 5 5 9. x y 5 5 284 Chapter 3 Linear Functions Version: Fall 2007 10. x y 5 5 11. x y 5 5 12. x y 5 5 13. Kate makes $39 , 000 per year and gets a raise of $1000 each year. Since her salary depends on the year, let time t represent the year, with t = 0 being the present year, and place it along the hor izontal axis. Let salary S , in thousands of dollars, be the dependent variable and place it along the vertical axis. We will assume that the rate of increase of $1000 per year is constant, so we can model this situation with a linear func tion. a) On a sheet of graph paper, make a graph to model this situation, going as far as t = 10 years. b) What is the Sintercept? c) What is the slope? d) Suppose we want to predict Kate’s salary in 20 years or 30 years. We cannot use the graphical model be cause it only shows up to t = 10 years. We could draw a larger graph, but what if we then wanted to predict 50 years into the future? The point is that a graphical model is limited to what it shows. A model algebraic function, however, can be used to pre dict for any year! Find the slopeintercept form of the linear function that models Kate’s salary. e) Write the function using function no tation, which emphasizes that S is a function of t . f) Now use the algebraic model from (e) to predict Kate’s salary 10 years, 20 years, 30 years, and 50 years into the future. g) Compute S(40). h) In a complete sentence, explain what the value of S (40) from part (g) means in the context of the problem. 14. For each DVD that Blue Charles Co. sells, they make 5 c profit. Profit depends on the number of DVD’s sold, Section 3.3 Equations of Lines 285 Version: Fall 2007 so let number sold n be the independent variable and profit P , in $, be the depen dent variable....
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 Slope, Linear function

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