Final answer:
The slope in the equation y = 0.68x + 70 represents the rate at which the cost to rent a moving truck increases per mile driven, and is $0.68 per mile. This concept of slope as a rate of change is a foundational element of linear equations in various contexts.
Step-by-step explanation:
The equation y = 0.68x + 70 models the cost to rent a moving truck, where y is the total cost and x is the number of miles driven. The slope of this linear equation represents the rate of change of the total cost with respect to the number of miles driven. In this case, the slope is 0.68, which means for every mile driven, the cost to rent the truck increases by $0.68. This is similar to how the slope in another equation, such as y = 55x + 75, represents the labor charges per hour of work done on a car. The y-intercept in the truck rental equation, which is 70, indicates the base cost of renting the truck before any miles are driven.
In understanding the importance of slope, consider another example where the slope is negative, indicating that increasing one good requires giving up some of the other, such as the opportunity cost between bus tickets and burgers. If we have a slope of -1.5 in an equation that models stock prices over time, it means the stock loses value at a rate of $1.50 per hour, as in the equation y = -1.5x + 15. In all these examples, the slope is crucial for interpreting the relationship between the two variables in a linear equation.