Final answer:
When x is multiplied by 2 in the equation y = kx^2, y will be multiplied by 4. Therefore, the correct answer is a) be multiplied by 4.
Step-by-step explanation:
The pattern between x and y in the equation y = kx^2 is that they are directly proportional. When x is multiplied by 2, y will be multiplied by 2^2, which is equal to 4.
Let's analyze the relationship between \( x \) and \( y \) based on the provided equation: \[ y = kx^2 \] where \( k \) is some constant.
Now, if we multiply \( x \) by 2, then \( x \) becomes \( 2x \). Let's substitute \( x \) with \( 2x \) in the equation and observe what happens: \[ y_{new} = k(2x)^2 \]
When we simplify the expression inside the square, we have to square both the 2 and \( x \) because they are both being raised to the power of 2: \[ y_{new} = k \cdot (2^2 \cdot x^2) \] \[ y_{new} = k \cdot (4 \cdot x^2) \] Since \( 4 \cdot x^2 \) means that the original \( x^2 \) is multiplied by 4, the new value of \( y \), which we can call \( y_{new} \), is now 4 times the original value of \( y \).
Therefore, if \( x \) was multiplied by 2, \( y \) would be multiplied by 4, because the square of 2 is 4. The complete sentence to describe the pattern between \( x \) and \( y \) is: If \( x \) was multiplied by 2, \( y \) would a) be multiplied by 4. Therefore, the correct answer is a) be multiplied by 4.