Question

If y varies inversely as x, and y = 5 as x = -2, find y for the x-value of 3.

Answer 1

If y varies inversely as x, then you'll have it as
\[y = \frac{1}{x}k\]
where k is the constant of proportionality
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Given that y=5 when x=-2, substitute to the above function to find 'k'
\[y = \frac{1}{x}k\]
\[5 = \frac{ 1 }{ -2 } k \]
Cross multiply -2
\[5(-2) = k\]
\[k = -10\]
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Using the same relation but when x=3, y=?
\[y = \frac{1}{x}k\]
Substitute x=3 and k=-10
\[y = \frac{1}{x}k\]
\[y = \frac{1}{3}(-10)\]
\[y=?\]