Reflect on your journey as a student. Express your reflection by following the
instructions below.
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Answer:
Short Story: The price of an apple in the market is $5 per kg. The expense I spend on apples varies directly with the mass of apple I buy.
Mathematical Equation: Let the mass of apple = [tex]x[/tex] kg. Let the total expense = [tex]y[/tex]. Then [tex]y = 5x[/tex].
Variation Statement: The expense of an apple varies directly with the mass of the apple; the constant is 5.
Step-by-step explanation:
Equations with direct and inverse variation sound a little intimidating, but really, they’re just two different ways of talking about how one number changes relative to another number.
As one number increases, so does the other in a direct variation. That is also called direct proportion: they’re the same thing. An example of this is the relationship between age and height. As the age in years of a child increases, the height will also increase.
The abstract can express direct variation using the equation [tex]y = kx[/tex].
[tex]x[/tex] and [tex]y[/tex] are the two quantities – in our example, they’d be the child’s age and height. [tex]k[/tex] is called the constant of proportionality: it tells you precisely how much bigger [tex]y[/tex] will get for every increase in [tex]x[/tex]. For example, maybe [tex]y = 2x[/tex]: this means that for every increase in [tex]x[/tex], y will increase by double that amount.
You can see that the bigger the number you plug in for [tex]x[/tex], the bigger the resulting value of [tex]y[/tex] will be.
In an inverse variation, it’s precisely the opposite: as one number increases, the other decreases. That is also called inverse proportion. An example would be the relationship between time spent wasting time in class and your grade on the midterm. The more you waste time, the lower your score on the test.
If we wanted to give this one an equation, we would say: [tex]y = \frac{k}{x}[/tex], where [tex]x[/tex] and [tex]y[/tex] are the two quantities, and [tex]k[/tex] is still the constant of proportionality, telling how much one varies when the other changes.
In this equation, you can see that you divide a constant number by [tex]x[/tex] to get the value of [tex]y[/tex]. So the bigger the value of [tex]x[/tex], the smaller the value of [tex]y[/tex] will be. That’s inverse variation: as one goes up, the other goes down.
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