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

Question

shinalcantara · Answer

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
$$y = \frac{1}{x}k$$
$$y = \frac{1}{3}(-10)$$
$$y=?$$