Solving Direct Variation Problems

As the numbers for a problem can be scored is fixed, it is a constant = K = \(\frac\) = 10For solving 5 problems total numbers scored T = KN = 10 x 5 = 50.From the above example we can understand that the ratio of two variables is a constant K and T, N are the variables which changes in proportion with value of constant.When two variables change in proportion it is called as direct variation.

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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.

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.

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 ).Direct variation word problems may be solved using the following steps: 1) Recognizing the word problem consists of direct variation as exemplified by presence of verbiage listed above; 2) Writing an equation containing known values for both variables resulting in an expression containing only the unknown representing the constant of proportionality; 3) Solving the equation for the constant of proportionality; 4) Using the calculated constant of proportionality to determine the value of one of the variables given the other.The amount of money raised at a charity fundraiser is directly proportional to the number of attendees.This is symbolically written as, A ∝ B (read as, ‘A varies as B’ ).Like in a math examination if for one problem solving we can score 10 numbers, so five problems solving we can get 50 numbers.The speed of a car and the distance traveled in a certain amount of time.The following statements are equivalent * y varies directly as x * y is directly proportional to x * y = kx for some constant k What is the direct variation formula? If a gallon of gas costs .25, how many gallons could you purchase for ? Now, they give us more information, and this will help us figure out what k is.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.


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