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3.7 – Variation

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

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3.7 – Variation

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  1. 3.7 – Variation Direct Variation: y varies directly as x(y is directly 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

  2. 3.7 – Variation 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 13 5 3 9 9 15 27 39

  3. 3.7 – Variation 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

  4. 3.7 – Variation 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.

  5. 3.7 – Variation 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 10 18 9 3 6 2 1.8 1

  6. 3.7 – Variation 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

  7. 3.7 – Variation 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.

  8. 3.7 – Variation 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.

  9. 3.7 – Variation 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? V varies jointly as h and . V = 402.12 cubic inches, h = 8 inches and r = 4 inches. Find V when h = 10 and r = 2.

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

  11. 4.1 - Systems of Linear Equations in Two Variables 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.

  12. 4.1 - Systems of Linear Equations in Two Variables 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.

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

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

  15. 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)

  16. 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) Solution

  17. 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) Solution

  18. 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) Solution

  19. 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) True Statement Solution: All reals Lines are the same

  20. 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) False Statement No Solution lines are parallel

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

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

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

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