Questions: If y varies directly as x and y=-88 when x=2, find y if x=28. (Round off your answer to the nearest hundredth.)

Solution Steps

To solve this problem, we need to use the concept of direct variation. If \( y \) varies directly as \( x \), it means \( y = kx \) for some constant \( k \). First, we find \( k \) using the given values \( y = -88 \) and \( x = 2 \). Then, we use this constant to find the new value of \( y \) when \( x = 28 \).

The problem states that \( y \) varies directly as \( x \). This means we can express the relationship as \( y = kx \), where \( k \) is a constant.

We are given that \( y = -88 \) when \( x = 2 \). Using the equation \( y = kx \), we can solve for \( k \): \[ k = \frac{y}{x} = \frac{-88}{2} = -44 \]

Now that we have \( k = -44 \), we can find the value of \( y \) when \( x = 28 \) using the equation \( y = kx \): \[ y = -44 \times 28 = -1232 \]

The problem asks us to round the answer to the nearest hundredth. Since \(-1232\) is already an integer, it remains \(-1232.00\) when rounded to the nearest hundredth.

Final Answer