Answer:
The concept of direct variation is summarized by the equation below.
We say that yy varies directly with xx if yy is expressed as the product of some constant number kk and xx.
However, the value of kk can’t equal zero, i.e. k \ne 0k
=0.
Case 1: k > 0k>0 (kk is positive)
If xx increases then the value of yy also increases, or if xx decreases then the value of yy also decreases.
Case 2: k < 0k<0 (kk is negative)
If xx increases then the value of yy decreases, or if xx decreases then the value of yy increases.
If we isolate kk on one side, it reveals that kk is the constant ratio between yy and xx. In other words, dividing yy by xx always yields a constant output.
k=y/x
kk is also known as the constant of variation, or constant of proportionality.
Examples of Direct Variation
Example 1: Tell whether yy varies directly with xx in the table below. If yes, write an equation to represent the direct variation.
Solution:
To show that yy varies directly with xx, we need to verify if dividing yy by xx always gives us the same value.
Since we always arrived at the same value of 22 when dividing yy by xx, we can claim that yy varies directly with xx. This constant number is, in fact, our k = 2k=2.
To write the equation of direct variation, we replace the letter kk by the number 22 in the equation y = kxy=kx.
Step-by-step explanation:
