Final answer:
The equation that represents the increase in sales is obtained by calculating the slope, which is the yearly increase in sales, and the y-intercept, which is the initial sales value. We found the slope to be $39,758 per year, with a starting value of $85,423, for the equation y = 39,758x + 85,423. None of the provided options match this equation.
Step-by-step explanation:
To find the equation for the line that represents the increase in sales for the winter coat company, we need to determine the slope (rate of increase) and the y-intercept (starting sales value). The slope is calculated by finding the change in sales over the change in years. The sales increased from $85,423 in 2013 to $323,972 in 2019, which is a difference of $238,549 over 6 years (2019 - 2013).
The slope (m) can be calculated as $238,549 / 6 years = $39,758 per year. The y-intercept (b) is the sales at the starting year, which is $85,423. Thus, the linear equation that models the sales of the company over the years is y = 39,758x + 85,423. None of the options A, B, C, or D match this equation, so we cannot choose any of them as the correct equation.