Instructions: y𝑦 varies directly with x𝑥. If y=−4𝑦=−4 when x=2𝑥=2, find y𝑦 when x=−6𝑥=−6. State the equation. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12−12). Equation: y=𝑦= Solution: y=
Question
Instructions: y𝑦 varies directly with x𝑥. If y=−4𝑦=−4 when x=2𝑥=2, find y𝑦 when x=−6𝑥=−6. State the equation. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12−12). Equation: y=𝑦= Solution: y=
Solution
The problem states that y varies directly with x. This means that y = kx for some constant k.
Step 1: Find the constant of variation (k) We know that when y = -4, x = 2. We can substitute these values into the equation to find k. -4 = k * 2 Solving for k, we get k = -4 / 2 = -2
Step 2: Find y when x = -6 Now that we know k, we can substitute x = -6 into the equation to find y. y = -2 * -6 y = 12
So, the equation is y = -2x and when x = -6, y = 12.
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