1. Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such th at 3.7 – Variation The number k is called the constant of variation or the constant of proportionality Verbal PhraseExpression

2. Direct Variation Suppose y varies directly as x. If y is 24 when x is 8, find the constant of variation (k) and the direct variation equation. direct variation equation constant of variation x y 3 9 5 15 9 27 13 39 3.7 – Variation

3. Hooke’s law states that the distance a spring stretches is directly proportional to the weight attached to the spring. If a 56-pound weight stretches a spring 7 inches, find the distance that an 85-pound weight stretches the spring. Round to tenths. direct variation equation constant of variation 3.7 – Variation

4. Inverse Variation: y varies inversely as x (y is inversely proportional to x), if there is a nonzero constant k such that The number k is called the constant of variation or the constant of proportionality. Verbal PhraseExpression 3.7 – Variation

5. Inverse Variation Suppose y varies inversely as x. If y is 6 when x is 3, find the constant of variation (k) and the inverse variation equation. direct variation equation constant of variation x y 3 6 9 2 10 1.8 18 1 3.7 – Variation

6. The speed r at which one needs to drive in order to travel a constant distance is inversely proportional to the time t. A fixed distance can be driven in 4 hours at a rate of 30 mph. Find the rate needed to drive the same distance in 5 hours. direct variation equation constant of variation 3.7 – Variation

7. Joint Variation If the ratio of a variable y to the product of two or more variables is constant, then y varies jointly as, or is jointly proportional, to the other variables. Verbal PhraseExpression 3.7 – Variation

8. Joint Variation z varies jointly as x and y. x = 3 and y = 2 when z = 12. Find z when x = 4 and y = 5. 3.7 – Variation

9. Joint Variation The volume of a can varies jointly as the height of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12 cubic inches. What is the volume of a can that has a 2 inch radius and a 10 inch height? 3.7 – Variation

10. A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 4.1 - Systems of Linear Equations in Two Variables

11. Determine whether (3, 9) is a solution of the following system. Both statements are true, therefore (3, 9) is a solution to the given system of linear equations. 4.1 - Systems of Linear Equations in Two Variables

12. Determine whether (3, -2) is a solution of the following system. Both statements are not true, therefore (3, -2) is not a solution to the given system of linear equations. 4.1 - Systems of Linear Equations in Two Variables

13. Solving Systems of Linear Equations by Graphing 4.1 - Systems of Linear Equations in Two Variables

14. Solving Systems of Linear Equations by Graphing 4.1 - Systems of Linear Equations in Two Variables

15. Solving Systems of Linear Equations by the Addition Method 4.1 - Systems of Linear Equations in Two Variables (Also referred to as the Elimination Method)

16. Solution 4.1 - Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

17. Solution 4.1 - Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

18. Solution 4.1 - Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

19. True Statement 4.1 - Systems of Linear Equations in Two Variables Solution: All reals Lines are the same Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

20. 4.1 - Systems of Linear Equations in Two Variables lines are parallel False Statement No Solution Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

21. Solving Systems of Linear Equations by Substitution Solution 4.1 - Systems of Linear Equations in Two Variables

22. Solving Systems of Linear Equations by Substitution Solution 4.1 - Systems of Linear Equations in Two Variables

23. Example 4.1 - Systems of Linear Equations in Two Variables LCD: 6 LCD: 15 Solution