Q. Assume that y varies inversely with x. If y=3 when x=8, find y when x=4. 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=3 when x=8. Substitute these values into the inverse variation equation to find k. 3=8k
Solve for k: Solve for k.To find k, multiply both sides of the equation by 8.3×8=k24=k
Write Inverse Variation Equation: Write the inverse variation equation with the found value of k. Now that we know k=24, the inverse variation equation is y=x24.
Find y for x=4: Find y when x=4.Substitute x=4 into the inverse variation equation to find y.y=424y=6
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