Questions: Find the variation constant and an equation of variation where y varies directly as x and y=50 when x=5 The variation constant is k= . The equation of variation is y= .

Solution Steps

To solve this problem, we need to understand that when \( y \) varies directly as \( x \), it means \( y = kx \) for some constant \( k \). Given that \( y = 50 \) when \( x = 5 \), we can substitute these values into the equation to solve for \( k \). Once \( k \) is found, we can write the equation of variation.

Given that \( y \) varies directly as \( x \), we can express this relationship as: \[ y = kx \] Substituting the provided values \( y = 50 \) and \( x = 5 \) into the equation, we have: \[ 50 = k \cdot 5 \] To find \( k \), we rearrange the equation: \[ k = \frac{50}{5} = 10.0 \]

Now that we have determined the variation constant \( k \), we can write the equation of variation: \[ y = 10.0x \]

Final Answer