In the context of the linear equation \( y = \frac{1}{4} x + 3 \), where \( y \) represents revenue in millions and \( x \) represents units sold, we can interpret the slope and y-intercept as follows:
1. Slope (\( \frac{1}{4} \)):
The slope of \( \frac{1}{4} \) indicates that for every additional unit sold, the revenue increases by \( 0.25 \) million dollars, or \( 250,000 \) dollars. This means that there is a positive relationship between the number of units sold and revenue: as sales increase, the revenue grows, albeit at a gradual rate. It highlights that while selling more units contributes to revenue, the increase in revenue per unit sold is relatively modest.
2. Y-intercept (0, 3):
The y-intercept, \( 3 \), signifies the expected revenue when no units are sold (i.e., when \( x = 0 \)). In this context, it means that even without selling any units, the business can anticipate a revenue of \( 3 \) million dollars. This could represent fixed income sources such as existing contracts, services, or baseline revenue that doesn’t depend on the volume of units sold.