Math Made Favourable

                                          Variation. In mathematics, variation explains how one quantity changes in relation to another. It helps us understand relationships like how time affects distance, or how speed affects fuel usage. There are four main types of variation: direct , inverse , joint , and partial (combined) variation. Let’s go through each type with detailed examples. 1. Direct Variation In direct variation , one quantity increases (or decreases) as the other increases (or decreases). If y  varies directly as x , the relationship is: y = k x where k k  is the constant of variation . Example 1 If y y  varies directly as x x , and y = 10 y = 10  when x = 5 x = 5 , find y y  when x = 8 x = 8 . Solution: y = k x y = kx Substitute y = 10 y = 10 , x = 5 x = 5 : 10 = 5 k ⇒ k = 2 10 = 5k \Rightarrow k = 2 When x = 8: y = 2 ( 8 ) =...