Chap3 Section3

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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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 y -intercept of the graph of the given linear function. iii. Use the slope and y -intercept to draw the graph of the given linear function on your coordinate system. Label the y -intercept 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 y -intercept 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: 1 7. x y 5 5 8. x y 5 5 9. x y 5 5
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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 S -intercept? 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 slope-intercept 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.
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