Questions: 7) y=3x k=3 9) y/x=5 11) y=3/5 x

Transcript text: 7) $y=3x$ $k=3$ 9) $\frac{y}{x}=5$ 11) $y=\frac{3}{5} x$

Solution

Solution Steps

To find the constant of variation, we need to identify the relationship between the variables in each equation. For direct variation, the constant of variation $ k $ is the coefficient of $ x $ in the equation $ y = kx $. For inverse variation, the constant is found by multiplying the variables together, $ xy = k $.

For equation 7, $ y = 3x $, the constant of variation $ k $ is directly given as 3.
For equation 9, $ \frac{y}{x} = 5 $, the constant of variation $ k $ is 5.
For equation 11, $ y = \frac{3}{5}x $, the constant of variation $ k $ is $\frac{3}{5}$.

Step 1: Constant of Variation for Equation 7

For the equation $ y = 3x $, the constant of variation $ k $ is directly given as: \[ k_7 = 3 \]

Step 2: Constant of Variation for Equation 9

For the equation $ \frac{y}{x} = 5 $, we can express this as $ y = 5x $. Thus, the constant of variation $ k $ is: \[ k_9 = 5 \]

Step 3: Constant of Variation for Equation 11

For the equation $ y = \frac{3}{5}x $, the constant of variation $ k $ is: \[ k_{11} = \frac{3}{5} = 0.6 \]

Final Answer

The constants of variation are: \[ \boxed{k_7 = 3}, \quad \boxed{k_9 = 5}, \quad \boxed{k_{11} = 0.6} \]

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