To determine whether \( y \) varies directly with \( x \), we need to check if there is a constant ratio \( \frac{y}{x} \) for all the values of \( x \) and \( y \).
From the data in the table:
- When \( x = 0 \), \( y = 0 \): \( \frac{y}{x} \) is undefined (but because both are 0, it is consistent with direct variation).
- When \( x = 1 \), \( y = 4 \): \( \frac{y}{x} = \frac{4}{1} = 4 \)
- When \( x = 2 \), \( y = 8 \): \( \frac{y}{x} = \frac{8}{2} = 4 \)
- When \( x = 3 \), \( y = 12 \): \( \frac{y}{x} = \frac{12}{3} = 4 \)
Now, since the ratio \( \frac{y}{x} = 4 \) is constant (for \( x \neq 0 \)), we can conclude that \( y \) varies directly with \( x \).
The equation for the direct variation can be written as:
\[ y = kx \]
where \( k \) is the constant of variation. Here, \( k = 4 \).
Thus, the equation is:
\[ y = 4x \]
1 answer