Objectives:
1) Learn what direction variation means
2) To learn how to calculate the constant of variation, write a direct variation equation, and use this to solve for values of x or y
3) Apply this knowledge in writing a direct variation model
1) What two things vary directly when two variables, x and y for instance, vary according to some constant known as the constant of variation? In an algebraic form, y = kx is a model of direct variation where x and y vary directly according to the constant of variation, k. In other words, say that k was 4, then y would be four times what x would be. If x was 2 and k was 4, then y will be 8.
2) If you were given x and y and were told that they were in direct variation of each other and you had the job of finding the constant of variation, then we would just have to invoke a little variable manipulation. Let's say that x = 4 and y = 18. How would we solve for k? Well, using the model given above, let's first solve the equation for k.
Now, using this, how could we find out what y would be when x = 12? We would just use the constant of variation just found and substitute in the value of x.
To find out what x would be when y = 3/2 we would do something similar to above.
3) How can we use this to model an application? What if we had the following problem: It is known that the maximum distance a rabbit can hop varies directly with the rabbit's weight. From the data below, find the constant of variation and write a direct variation equation.
RabbitWeight 

















Now using this equation find out
a) What would be the maximum hopping distance for a 7 pound rabbit?
b) How much would a rabbit weigh if it could hop a maximum of 8.5 feet?
Solving part a...
Solving part b...
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