Instructions: The variables x𝑥 and y𝑦 vary directly, and y=15𝑦=15 when x=3𝑥=3. Find the equation and determine x when x=12.Equation: Solution: When x=12𝑥=12, y=𝑦=
Question
Instructions: The variables x𝑥 and y𝑦 vary directly, and y=15𝑦=15 when x=3𝑥=3. Find the equation and determine x when x=12.Equation: Solution: When x=12𝑥=12, y=𝑦=
Solution
The variables x and y vary directly, which means they follow the equation y = kx, where k is the constant of variation.
Step 1: Find the constant of variation (k) Given that y = 15 when x = 3, we can substitute these values into the equation to find k. 15 = k * 3 So, k = 15 / 3 = 5
Step 2: Write the equation Now that we know k = 5, we can write the equation as y = 5x.
Step 3: Find y when x = 12 Substitute x = 12 into the equation to find y. y = 5 * 12 = 60
So, the equation is y = 5x and when x = 12, y = 60.
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