Bab 1 (part 1) Matematik Tingkatan 5 KSSM : 1.1 Ubahan Langsung

Introduction

This tutorial provides a step-by-step guide to understanding direct variation, a fundamental concept in mathematics, particularly useful in solving problems involving two variables. By the end of this guide, you will be able to identify direct variation and formulate equations that represent it.

Step 1: Understanding Direct Variation

Direct variation occurs when two variables are related such that when one variable changes, the other variable changes in a predictable way. Here’s how to identify it:

• Definition: If ( y ) varies directly with ( x ), it can be expressed as: [ y = kx ] where ( k ) is a constant known as the constant of variation.

• Identifying Direct Variation:

  • Check if the ratio of ( y ) to ( x ) is constant.
  • If ( \frac{y}{x} = k ) remains the same for all data points, then ( y ) varies directly with ( x ).

Practical Tip

To confirm direct variation in data, create a table of values for ( x ) and ( y ) and calculate the ratio ( \frac{y}{x} ). If the ratios are equal, you have a direct variation.

Step 2: Formulating the Equation

Once you've established that a direct variation exists, the next step is to formulate the equation.

• Using the Constant of Variation:
  • Identify ( k ) using one of the known pairs of ( (x, y) ).
  • For example, if ( x = 2 ) and ( y = 8 ): [ k = \frac{y}{x} = \frac{8}{2} = 4 ]
  • Hence, the equation becomes: [ y = 4x ]

Step 3: Graphing Direct Variation

Visual representation can enhance understanding.

• Steps to Graph:
  • Plot the point ( (x, y) ) based on the equation ( y = kx ).
  • Draw a straight line through the origin (0,0), as direct variation always passes through this point.

Common Pitfalls

• Failing to include the origin in the graph can lead to misunderstandings about direct variation.
• Mixing up direct variation with other types of relationships, such as inverse variation.

Step 4: Real-World Applications

Direct variation can be observed in various real-life scenarios.

• Examples include:
  • Speed and distance traveled.
  • Cost and quantity of items purchased.

Understanding these applications can help solidify the concept.

Conclusion

In this tutorial, you learned how to recognize and formulate equations for direct variation. By identifying the constant of variation and graphing the relationship, you can apply this knowledge to solve mathematical problems effectively. As a next step, practice with different sets of values to deepen your understanding of direct variation and its applications in real-world scenarios.