Solving Inverse Variation Problems: Equation, Examples, and Questions, Slides of Mathematics

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INVERSE

VARIATION

𝑦 = 𝑘 𝑥 INVERSE VARIATION Let x and y denote two quantities. Y varies inversely with x, or y is inversely proportional to x, if there is a nonzero k such that:

Example 1: If y varies inversely as x, and y=1/3 when x=18, find the value of y when x=2. Solution: 𝑦^ =^ 𝑘 𝑥 18 𝑦 = 6 2 𝑦 = 3 𝑘 = (^6) 𝐻𝑒𝑛𝑐𝑒 , 𝑦 = 3 𝑤 𝑒𝑛h 𝑥 =2. 𝑦 = 6 𝑥

Example 2: If y varies inversely as x, and y=8 when x=20, find y when x=16. Solution: 8 = 𝑘 20 𝑇 𝑢𝑠 h , 𝑦 = 10 𝑤 𝑒𝑛h 𝑥 =16. 𝑦 = 10 𝑦 = 160 𝑥 𝑦 = 160 16

If y varies inversely as x, and y=4 when x=15, find the value of y when x=12.

If y varies inversely as x, when x=2, y=. Find the value of y when x=.

If y varies inversely as x, when x=0.1, y=0.01. Find the value of y when x=4.

If y varies inversely as x, when x=0.1, y=. Find the value of y when x=10.

If y varies inversely as x, when x=8, y=2. Find the value of y when x=10.

If y varies inversely as x, when x=12, y=3. Find the value of y when x=3.

If y varies inversely as x, when x=, y=. Find the value of y when x=2.

If y varies inversely proportional to the square of x, when x=8, y=. Find the value of y when x=.

If y varies inversely as the square root of x, when x=7, y=9. Find the value of x when y=.

If y varies inversely as x, when x=6, y=25. Find the value of y when x=.