Questions: Find the variation constant and an equation of variation where y varies directly as x and y=5 when x=32. The variation constant is 5/32 (Type an integer or a fraction.) The equation of variation is y=5.

Solution Steps

To solve this problem, we need to determine the variation constant and the equation of variation. Since \( y \) varies directly as \( x \), we can express this relationship as \( y = kx \), where \( k \) is the variation constant. Given that \( y = 5 \) when \( x = 32 \), 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 have the equation \( y = kx \), where \( k \) is the variation constant. We are provided with the values \( y = 5 \) and \( x = 32 \). Substituting these values into the equation, we get:

\[ 5 = k \times 32 \]

Solving for \( k \), we divide both sides by 32:

\[ k = \frac{5}{32} \approx 0.15625 \]

With the variation constant \( k \) determined, we can write the equation of variation as:

\[ y = \frac{5}{32}x \]

Final Answer