Q. Assume that y varies inversely with x. If y=4 when x=4, find y when x=2. Write and solve an inverse variation equation to find the answer.y= _____
Understand Relationship: Understand the relationship between y and x. Inverse variation means that as one variable increases, the other decreases proportionally. The formula for inverse variation is y=xk, where k is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation k. We are given that y=4 when x=4. Substitute these values into the inverse variation formula to find k. 4=4k
Solve for k: Solve for k.To find k, multiply both sides of the equation by 4.4×4=k16=k
Write Inverse Variation Equation: Write the inverse variation equation with the found value of k. Now that we know k=16, we can write the equation as y=x16.
Find y for x=2: Find y when x=2. Substitute 2 for x in the equation y=x16. y=216y=8
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