Bot GPT 4-o mini To find the constant of variation \( k \) of the line \( y = kx \) that passes through the points \( (3, 18) \) and \( (5, 30) \), we'll use the coordinates provided to establish the relationship.
The formula for the constant of variation can be found using either of the points provided. We'll start with the first point \( (3, 18) \).
Using the formula \( y = kx \):
- Substitute \( x = 3 \) and \( y = 18 \): \[ 18 = k \cdot 3 \] \[ k = \frac{18}{3} = 6 \]
Now let's verify with the second point \( (5, 30) \).
- Substitute \( x = 5 \) and \( y = 30 \): \[ 30 = k \cdot 5 \] Solving for \( k \): \[ k = \frac{30}{5} = 6 \]
In both cases, we find that \( k = 6 \).
Thus, the constant of variation \( k \) is \( \boxed{6} \).
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