Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?
If \( y \) varies directly with \( x \), the relationship between \( y \) and \( x \) can be described by the equation \( y = kx \), where \( k \) is the constant of variation (or the constant of proportionality).
Given that \( y = 24 \) when \( x = 8 \), we can find \( k \) by rearranging the equation to solve for \( k \):
\[ 24 = k \cdot 8 \]
\[ k = \frac{24}{8} \]
\[ k = 3 \]
Now that we know \( k \), we can predict \( y \) for any other value of \( x \). When \( x = 10 \), the value of \( y \) is:
\[ y = 3 \cdot 10 \]
\[ y = 30 \]
So when \( x = 10 \), the value of \( y \) is \( 30 \).