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Instructions: If y𝑦 varies inversely as x𝑥 and y=2𝑦=2 when x=8𝑥=8, find y𝑦 when x=2𝑥=2. Write the equation using the given information, then use the equation to solve for y𝑦. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12−12).

Question

Instructions: If y𝑦 varies inversely as x𝑥 and y=2𝑦=2 when x=8𝑥=8, find y𝑦 when x=2𝑥=2. Write the equation using the given information, then use the equation to solve for y𝑦. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12−12).

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Solution

Step 1: Understand the problem The problem states that y varies inversely as x. This means that as x increases, y decreases and vice versa. The relationship can be expressed as y = k/x, where k is the constant of variation.

Step 2: Write the equation using the given information We know that when x = 8, y = 2. We can substitute these values into the equation to find the constant of variation (k). So, 2 = k/8. Solving for k gives us k = 2 * 8 = 16.

Step 3: Use the equation to solve for y Now that we know k = 16, we can substitute this value and the given x value into the equation to find y. So when x = 2, y = 16/2 = 8.

Therefore, when x = 2, y = 8.

This problem has been solved

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