Section 2.4 Applications of Linear Equations and Modeling 171 Problem Recognition Exercises Characteristics of Linear Equations For Exercises 1–20, choose the equation(s) from column B whose graph satisfies the condition described in column A. Give all possible answers. 1. Line whose slope is positive. Column A Column B a. b. c. d. e. f. g. y 4x 2x 4y 4 y 1 3 x 3 3x 5y 10 3y 9 y 5x 1 4x 1 9 h. x 3y 12 2. Line whose slope is negative. 3. Line that passes through the origin. 4. Line that contains the point (2, 0). 5. Line whose y-intercept is (0,3). 6. Line whose y-intercept is (0, 0). 7. Line whose slope is 1 3 1 2 . 8. Line whose slope is . 9. Line whose slope is 0. 10. Line whose slope is undefined. 11. Line that is parallel to the line with equation x 3y 6. 12. Line perpendicular to the line with equation x 4y 4. 13. Line that is vertical. 14. Line that is horizontal. 15. Line whose x-intercept is (12, 0). 16. Line whose x-intercept is a1 5 , 0b. 17. Line that has no x-intercept. 18. Line that is perpendicular to the x-axis. 19. Line with a negative slope and positive y-intercept. 20. Line with a positive slope and negative y-intercept. Applications of Linear Equations and Modeling Section 2.4 1. Writing a Linear Model A mathematical model is a formula or equation that represents a relationship between two or more variables in a real-world application. Algebra (or some other field of mathematics) can then be used to solve the problem. The use of mathematical models is found throughout the physical and biological sciences, sports, medicine, economics, business, and many other fields. For an equation written in slope-intercept form, y mx b, the term mx is called the variable term.The value of this term changes with different values of x. The term b is called the constant term and it remains unchanged regardless of the value of x.The slope of the line, m, is called the rate of change.A linear equation can be created if the rate of change and the constant are known. Concepts 1. Writing a Linear Model 2. Interpreting a Linear Model 3. Finding a Linear Model from Observed Data Points
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