What is it and how do I know when I see it? Direct Variation What is it and how do I know when I see it?

Definition:   Two quantities are said to be in direct variation if an increase (or decrease) in one quantity results in increase (or decrease) in the other quantity. (i.e.) If two quantities vary always in the same ratio then they are in direct variation. In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

Examples of Direct Variation:

Examples of Direct Variation:

Examples of Direct Variation: Verify whether the following represent Direct variation or not: Time (Hrs) 2 5 4 3 Distance(Kms) 80 200 160 120 Solution: From the above examples time taken increases/Decreases, distance also increases/ decreases. Let us check whether the given table is direct variation.

Step 1: Sort the data in ascending order Time (Hrs) 2 3 4 5 Distance (Kms) 80 120 160 200  

Complete the table if they are in Direct variation Example2: Complete the table if they are in Direct variation 8 10 15 4 2 16 -  

Step 4: Hint: Denominator = Numerator x 2   8 10 15 4 2 16 20 30

Example 3: The cost of uniforms for twelve students is Rs.3,000. How many students can get uniform for Rs.1250. Solution: No of students Cost of the uniform 12 3000 ? 1,250 When money spent decreases ( ), the number of uniform also decreases ( ) . They are in direct variation.

Rule 1: In direct variation, we need to cross multiply the given information Step 1:     Step 4:    

Try these: 1. If the number of apples increases then the number of fruit boxes also_________ is called direct variation. 2. find the x value and also check whether the ratios are direct variations 12 : x = 300 : 125. 3. if x varies directly as y, complete the given table by direct variation. x 1 3 9 y 2 10 16