The Variation_Presentation_with_Graphs.pptx

For the grade 10 students

1. Illustrating Situations that Involve Variations Direct, Inverse, Joint, and Combined Variation

2. Objectives ✔ Define and differentiate between types of variations. ✔ Illustrate real-life situations for each type. ✔ Translate situations into mathematical expressions.

3. What is Variation? Variation shows how two or more quantities are related. Examples: - Cost vs. Quantity - Speed vs. Time

4. Direct Variation Definition: One quantity increases or decreases as the other increases or decreases. Equation: y = kx Example: The cost of apples varies directly with the number of kilos bought.

5. Inverse Variation Definition: One quantity increases as the other decreases. Equation: y = k/x Example: The time needed to finish a job varies inversely with the number of workers.

6. Joint Variation Definition: A quantity varies directly as the product of two or more other quantities. Equation: y = kxz Example: The volume of a rectangular solid varies jointly with its length, width, and height.

7. Combined Variation Definition: A quantity varies directly with one or more variables and inversely with another. Equation: y = (kx)/z Example: The intensity of light varies directly with brightness but inversely with the square of distance.

8. Summary Direct: y = kx (increase ↔ increase) Inverse: y = k/x (increase ↔ decrease) Joint: y = kxz (varies with more than one variable) Combined: y = (kx)/z (mix of direct and inverse)

9. Practice Exercise Identify the type of variation illustrated in the following situations: 1. The distance traveled varies directly with time when speed is constant. 2. The pressure of a gas varies inversely with its volume. 3. The area of a rectangle varies jointly with its length and width. 4. The time to finish a race varies directly with distance and inversely with speed.

10. Closing “Mathematics is the language in which we describe relationships.” Thank you!