The Consumer Price index (CPI), which measures the cost of a typical package of consumer goods, was 224.1 in 2011 and 238.7 in 2016 . Let \( x=11 \) correspond to the year 2011 and estimate the CPI in 2013 and 2015 Assume that the data can be modeled by a straight line and that the trend continues indefinitely Use two data points to find such a line and then estimate the requested quantities Let y represent the CPI. The linear equation that best models the CPI is (Simplity your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)

We are given two data points:  • When x = 11 (year 2011), the CPI y = 224.1  • When x = 16 (year 2016), the CPI y = 238.7 Step 1. Find the slope, m, of the line using the formula:  m = (y₂ - y₁) / (x₂ - x₁) Substitute the values:  m = (238.7 - 224.1) / (16 - 11)  m = 14.6 / 5  m = 2.92 Step 2. Write the linear equation in the form y = mx + b. We know m = 2.92. To find b (the y-intercept), plug in one of the points (using x = 11 and y = 224.1):  224.1 = 2.92(11) + b Calculate 2.92 × 11:  2.92 × 11 = 32.12 Thus,  224.1 = 32.12 + b Solve for b:  b = 224.1 - 32.12  b = 191.98 So, the linear equation is:  y = 2.92x + 191.98 Step 3. Estimate the CPI for the requested years. • For 2013 (x = 13):  y = 2.92(13) + 191.98  2.92 × 13 = 37.96  y = 37.96 + 191.98 = 229.94 • For 2015 (x = 15):  y = 2.92(15) + 191.98  2.92 × 15 = 43.80  y = 43.80 + 191.98 = 235.78 Final Answers: • The linear model is y = 2.92x + 191.98. • The estimated CPI for 2013 is 229.94. • The estimated CPI for 2015 is 235.78.