Solving Direct Variation Problems

Solving Direct Variation Problems-82
Direct variation is the simplest type of variation and in practical life we can find many situations which can be co-related with direct variation.If two variables A and B are so related that when A increases ( or decreases ) in a given ratio, B also increases ( or, decreases ) in the same ratio, then A is said to vary directly as B ( or, A is said to vary as B ).

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A direct variation is a linear equation that can be written in the form y = kx , where k is a nonzero constant. Determine the direct variation equation and then determine y when x = 3.5 2.

The number k is called the constant of proportionality or constant of variation. Hooke's Law states that the displacement, d, that a spring is stretched by a hanging object varies directly as the mass of the object.

Solution: As P varies directly with Q, ratio of P and Q is constant for any value of P and Q.

So constant K = \(\frac\) = \(\frac\) = \(\frac\)So the equation that describes the direct variation of P and Q is P = \(\frac\)Q.

But when the value of K is very small, Y changes very less with change of X.

For this case K is equivalent to the ratio of change of two variables. If P varies directly as Q and the value of P is 60 and Q is 40, what is the equation that describes this direct variation of P and Q?

There are many situations in our daily lives that involve direct variation.

The two quantities = 55.42 The cost for 95 km is .42 How to define direct variation and solve direct variation word problems?

Graphically, we have a line that passes through the origin with the slope of k. If the distance is 10 cm when the mass is kg, what is the distance when the mass is 5 kg?

We're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing. So if x is equal to 1-- this statement up here, a gallon of gas-- that tells us if we get 1 gallon, if x is equal to 1, then y is .25, right? They tell us 1 gallon costs .25, so you could write it right here, .25 is equal to k times x, times 1. So the equation, how y varies with x, is y is equal to 2.25x, where x is the number of gallons we purchase. Now if we want to solve for x, we can divide both sides by 2.25, so let's do that. So first of all, I just like to think of it as a fraction.


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