Final answer:
Graphs showing continuous changes—like temperature over time or an animal's mass with age—should be connected. For the mass of coins, connect the points if all coins are of the same type. For milk price versus carton size, the graph may not be connected if there are only specific sizes available.
Step-by-step explanation:
The question asks about which graphs should be connected when representing different relationships between variables. First, it is important to understand the concept of a function, which is a type of relationship whereby one variable consistently depends on another. In the contexts provided:
- Mass of a stack of coins based on the number of coins can be connected, assuming additional coins are of the same type, making the mass increase in discrete but uniform amounts.
- Temperature in Vancouver as a function of the time of day should be connected because temperature changes continuously over time.
- Mass of an animal as a function of age should be connected in general, as mass typically changes in a continuous manner as the animal grows.
- The price of a carton of milk based on the size of the carton might not be connected if prices are only set for certain standard carton sizes, resulting in a step-like function.
If you were to graph these scenarios using the linear equation y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept, each graph would illustrate how the dependent variable (e.g. mass, temperature, price) changes in relation to the independent variable (coin count, time of day, carton size).