Q. If y varies inversely with x and y=3 when x=4, find y when x=1. Write and solve an inverse variation equation to find the answer.y= _____
Identify general form: Given that y varies inversely with x. Identify the general form of inverse variation. In inverse variation, variables change in opposite directions. Inverse variation: y=xk
Substitute values in equation: We know that y=3 when x=4. Choose the equation after substituting the values in y=xk. Substitute 4 for x and 3 for y in y=xk. 3=4k
Solve for k: We found:3=4kSolve the equation to find the value of k.To isolate k, multiply both sides by 4.3×4=(4k)×412=k
Write inverse variation equation: We have:k=12Write the inverse variation equation in the form of y=xk.Substitute k=12 in y=xk.y=x12
Find y for x=1: Inverse variation equation:y=x12Find y when x=1.Substitute 1 for x in y=x12.y=112y=12
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