Algebra help?

Question

Could someone please explain to me inverse variations and direct variations? Then find the constant of variation.

a = -3b

I don't understand any of that....

Answer 1

if i buy an apple, it costs 20 cents, i i but 5, it costs a dollar. so the more apples, the more the cost
we say that the cost of apples varies directly with the number of apples
[the more the no. the more the cost]
now, if i drive at 2 mph, i take an hour to get to my home. but if i drive at 10 mph, i take just 20 min
we say that my speed varies inversely with time
[more speed, less time]
we represent variation with the greek letter Alpha
a alpha b means a varuies directly with b and a alpha (1/b) means a varies inversely with b
now, if 2 values vary, then they r not necessarily equal. but if we multiply one of them with a number, they become equal. that no is called the constant of variation (proportionality)
if a alpha b, then a = kb, where k is a constant
hence, k = a/b
if a alpha 1/b, the k = ab
why is it a constant
look at this example
1 apple costs 20 cents; k = 1/20
2 apples cost 40 cents; k = 2/40 = 1/20
3 apples cost 60 cents; k = 1/20
so, the ratio is always the same
now, a nd b might be variables, but k is ALWAYS a constant
AS FOR YOUR QUESTION
a=-3b
a and b are variables, and -3 is a constant
so the constant of variation for the relation a alpha b is -3 i.e., a/b = -3

Answer 2

Direct variation is when two things increase or decrease together. If you put more flour in the bowl, you will be able to make more bread. If you put less water in the pitcher, you will be able to make less lemonade. If you increase one quantity and the other also increases, it's direct variation. Similarly, if you decrease one quantity and the other decreases as well, it's direct variation.

Inverse variation is the opposite. When you increase one quantity, you decrease the second. An example might be that as you increase the number of police officers on patrol in a given area, the number of crimes reported in that area goes down. Or as you decrease the number of insects in your garden, the number of vegetables you harvest increases.

Another real life example is the formula for rate. Rate equals distance divided by time or r = d/t. Rate and distance vary directly because if you travel for the same amount of time, as you increase your rate, the distance you travel will increase over that time period. OTOH, rate and time vary inversely because if you are going to travel a constant distance, it will take you more time to cover that distance as your rate decreases.

Equations that look like y = kx (where k is a constant, or a number) are direct variation situations while equations that look like y = k/x are indirect variation situations. If one of the two things you are looking at is in the denominator of a fraction, it's indirect variation (plug in numbers and you'll see that as x gets bigger, the fraction and therefore y get smaller). You can make the formulae more complex, like y = kx^2, but the general relationships still hold... The area of a circle = pi times radius squared so we say the area of the circle varies directly with the square of the radius.

The constant is just the number(s) out in front of the variables you are interested in. Sometimes in science classes you will use a letter called a constant that is defined as having a specific number value... the constant is the part of the equation that doesn't change when you plug different numbers in for the variables in the equation. Every time you do a different calculation with different numbers, the constant always stays the same (or constant!) The variables are the letters and the constants is the number in the example you give above.

Answer 3

http://www.mathwords.com/i/inverse_variation.htm