Instructions: The variables x𝑥 and y𝑦 vary inversely, and y=7𝑦=7 when x=2𝑥=2. Write an equation that relates x𝑥 and y𝑦 and find y𝑦 when x=−6𝑥=−6. Enter any fractions using the forward slash (i.e. “/”; -1/2 is the same as −12−12). Reduce all fractions.Equation: Answer 1 Question 12Solution: When x=−6𝑥=−6, y=
Question
Instructions: The variables x𝑥 and y𝑦 vary inversely, and y=7𝑦=7 when x=2𝑥=2. Write an equation that relates x𝑥 and y𝑦 and find y𝑦 when x=−6𝑥=−6. Enter any fractions using the forward slash (i.e. “/”; -1/2 is the same as −12−12). Reduce all fractions.Equation: Answer 1 Question 12Solution: When x=−6𝑥=−6, y=
Solution
The relationship between x and y in inverse variation can be written as xy = k, where k is the constant of variation.
From the problem, we know that y = 7 when x = 2. We can substitute these values into the equation to find the constant of variation:
2*7 = k k = 14
So, the equation that relates x and y is xy = 14.
To find the value of y when x = -6, we substitute these values into the equation:
-6*y = 14 y = 14 / -6 y = -7/3
So, when x = -6, y = -7/3.
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