In 2018 , the citizens of a country spent a total of \( \$ 73.6 \) billion on their pets. In 2015 , the citizens of the same country spent \( \$ 66.79 \) billion on their pets. Let \( y \) be the amount spent by those citizens on their pets in year \( x \), where \( x=0 \) represents the year 2015 . a. Write a linear equation that models the amount the citizens of the country spent on their pets in the year \( x \). [Hint: The line must pass through the points \( (0,66.79) \) and \( (3,73.6) \).] b. Use this equation to predict the amount citizens spend on their pets in 2027 .

To solve the problem, we will first find the linear equation that models the amount spent on pets over the years. ### Part a: Write a linear equation We have two points: - \( (0, 66.79) \) representing the year 2015 - \( (3, 73.6) \) representing the year 2018 We can use the slope-intercept form of a linear equation, which is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. **Step 1: Calculate the slope \( m \)** The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \( (0, 66.79) \) and \( (3, 73.6) \): \[ m = \frac{73.6 - 66.79}{3 - 0} = \frac{6.81}{3} = 2.27 \] **Step 2: Write the equation** Now that we have the slope \( m = 2.27 \) and the y-intercept \( b = 66.79 \), we can write the equation: \[ y = 2.27x + 66.79 \] ### Part b: Predict the amount spent in 2027 To predict the amount spent in 2027, we need to find the value of \( x \) for that year. Since \( x = 0 \) corresponds to 2015, we can calculate \( x \) for 2027: \[ x = 2027 - 2015 = 12 \] Now we substitute \( x = 12 \) into the equation: \[ y = 2.27(12) + 66.79 \] Calculating this: \[ y = 27.24 + 66.79 = 94.03 \] Thus, the predicted amount that citizens will spend on their pets in 2027 is: \[ \boxed{94.03 \text{ billion dollars}} \]