3) This table shows the relationship between \( x \) and \( y \). \( x \quad y \) \( 5 \quad 1275 \) \( 9 \quad 229.5 \) 12306 Which equation models this relationship? (A) \( y=24 x \) (B) \( y=24.5 x \) (C) \( y=25 x \) (D) \( y=25.5 x \)

To determine which equation models the relationship between \( x \) and \( y \), we can analyze the given data points and check which equation fits best. The data points provided are: - When \( x = 5 \), \( y = 1275 \) - When \( x = 9 \), \( y = 229.5 \) We can calculate the value of \( y/x \) for both points to see if it corresponds to any of the options given. 1. For the first point: \[ \frac{y}{x} = \frac{1275}{5} \] 2. For the second point: \[ \frac{y}{x} = \frac{229.5}{9} \] Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(\frac{1275}{5}\) - step1: Reduce the numbers: \(\frac{255}{1}\) - step2: Calculate: \(255\) Calculate or simplify the expression \( 229.5/9 \). Calculate the value by following steps: - step0: Calculate: \(\frac{229.5}{9}\) - step1: Convert the expressions: \(\frac{\frac{459}{2}}{9}\) - step2: Multiply by the reciprocal: \(\frac{459}{2}\times \frac{1}{9}\) - step3: Reduce the numbers: \(\frac{51}{2}\times 1\) - step4: Multiply: \(\frac{51}{2}\) Calculating the values: 1. For the first point: \[ \frac{1275}{5} = 255 \] 2. For the second point: \[ \frac{229.5}{9} = 25.5 \] Now, we can summarize the results: - For \( x = 5 \), \( y = 255x \) - For \( x = 9 \), \( y = 25.5x \) Since the values of \( y/x \) are not consistent across the two points, we need to check the equations provided in the options to see which one fits the second point, as it seems more reasonable given the smaller \( x \) value. The options are: (A) \( y = 24x \) (B) \( y = 24.5x \) (C) \( y = 25x \) (D) \( y = 25.5x \) Since \( y = 25.5x \) matches the second point, we can conclude that the equation that models this relationship is: **(D) \( y = 25.5x \)**.