Instructions: If y𝑦 varies directly as x𝑥 and y=−16𝑦=−16 when x=4𝑥=4, find y𝑦 when x=9𝑥=9. 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 directly as x𝑥 and y=−16𝑦=−16 when x=4𝑥=4, find y𝑦 when x=9𝑥=9. 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).
Solution
First, let's understand what it means when we say "y varies directly as x". This means that y = kx for some constant k.
Given that y = -16 when x = 4, we can substitute these values into the equation to find the value of k.
So, -16 = k*4. Solving for k, we get k = -16/4 = -4.
Now we have the equation y = -4x.
We can use this equation to find the value of y when x = 9.
Substituting x = 9 into the equation, we get y = -4*9 = -36.
So, when x = 9, y = -36.
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