c. What do the slope and y-intercept mean in the context of this problem?
Hint: What do you pay when you step into the cab?
In the context of this problem, the slope and y-intercept refer to the equation of a line that represents the relationship between the cost of riding a cab and the distance traveled. The slope represents the rate at which the cost increases per unit of distance, while the y-intercept represents the initial cost when you step into the cab.
To understand the slope and y-intercept, you should first have the equation of the line that represents the relationship between the cost and distance. This equation is typically in the form of y = mx + b, where y represents the cost, x represents the distance, m represents the slope, and b represents the y-intercept.
To determine the slope of the line, you need to find the change in cost divided by the change in distance. You can do this by choosing two points on the line, looking at their respective costs and distances, and then calculating the difference between them. Dividing this difference in cost by the difference in distance will give you the slope.
The y-intercept, on the other hand, represents the initial cost when you step into the cab. It is the value of y when x is equal to 0. In other words, it is the cost you pay before any distance is traveled.
Once you have the equation of the line, you can interpret the slope as the cost increase for each unit of distance traveled. For example, if the slope is $2, it means that for every additional unit of distance traveled (such as one mile), the cost of the cab ride would increase by $2.
The y-intercept, or the initial cost, represents the amount you have to pay even before you start traveling any distance. For instance, if the y-intercept is $5, it means that when you step into the cab, you would have to pay $5 regardless of the distance you will travel.