Direct variation is a mathematical relationship between two variables where one quantity changes in direct proportion to the other. This means if one variable increases, the other increases by the same factor, and if one decreases, the other decreases proportionately. In other words, the ratio of the two variables remains constant
. The relationship is expressed as:
y=kxy=kxy=kx
where yyy and xxx are the variables, and kkk is the constant of proportionality (a nonzero constant). The symbol for direct variation is y∝xy\propto xy∝x, meaning yyy varies directly as xxx
. Key points about direct variation:
- It is a linear relationship, so its graph is a straight line passing through the origin.
- The constant kkk can be found by dividing yyy by xxx when x≠0x\neq 0x=0.
- Real-life examples include the relationship between the circumference and diameter of a circle, or the amount earned based on hours worked
In summary, direct variation means two quantities increase or decrease together at a constant ratio, described by the formula y=kxy=kxy=kx
