For each equation determine whether it shows a direct variation (that Is, shows directly proportional variables) If it does, find the constant of variation and write it in simplest form. 16y=2x Direct variation k=square Not direct variation 24x-3y=0 Direct variation k=square Not direct variation

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For each equation determine whether it shows a direct variation (that Is, shows directly proportional variables) If it does, find the constant of variation and write it in simplest form. 16y=2x Direct variation k=square Not direct variation 24x-3y=0 Direct variation k=square Not direct variation

Answer 1

Let's tackle each equation one by one.**Equation 1:**\[16y = 2x\]To determine if this is a direct variation, we need to see if we can express \(y\) as \(y = kx\) where \(k\) is the constant of variation.Let's solve for \(y\) in terms of \(x\):\[y = \frac{2}{16}x\]\[y = \frac{1}{8}x\]Since we can express \(y\) as a multiple of \(x\), this is a direct variation.The constant of variation \(k\) is:\[k = \frac{1}{8}\]**The direct variation equation is \(y = \frac{1}{8}x\) and the constant of variation is \(k = \frac{1}{8}\).****Equation 2:**\[24x - 3y = 0\]To determine if this is a direct variation, we need to isolate \(y\) and see if it can be expressed in the form \(y = kx\).Let's solve for \(y\):\[3y = 24x\]\[y = 8x\]Since \(y\) can be expressed as a multiple of \(x\), this is also a direct variation.The constant of variation \(k\) is:\[k = 8\]**The direct variation equation is \(y = 8x\) and the constant of variation is \(k = 8\).**

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For each equation determine whether it shows a direct variation (that Is, shows directly proportional variables) If it does, find the constant of variation and write it in simplest form. 16y=2x Direct variation k=square Not direct variation 24x-3y=0 Direct variation k=square Not direct variation

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