Solving Direct Variation Problems

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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 $2.25, right? They tell us 1 gallon costs $2.25, so you could write it right here, $2.25 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.

When two variables change in proportion it is called as direct variation.

In direct variation one variable is constant times of other.

Some examples of direct variation problems in real life: The number of hours you work and the amount of your paycheck.

The amount of weight on a spring and the distance the spring will stretch.

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?

If one variable increases other will increase, if one decrease other will also decease.

This means that the variables change in a same ratio which is called as constant of variation.


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