Q. If y varies inversely with x and y=4 when x=8, 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. Since y varies inversely with x, the relationship can be described by the equation 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=8. Substitute these values into the inverse variation equation to find k. 4=8k Now, solve for k by multiplying both sides by 8. 4×8=kk=32
Write Inverse Variation Equation: Write the inverse variation equation with the found constant k. Now that we have found k to be 32, the inverse variation equation is y=x32.
Find y for x=2: Find y when x=2 using the inverse variation equation.Substitute x=2 into the equation y=x32.y=232y=16
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