Final answer:
The unit rate and slope of a proportional relationship are related because they both represent the rate of change, the constant of proportionality, and the steepness of the line on a graph.
Step-by-step explanation:
The unit rate and slope of a proportional relationship are related to each other for several valid reasons:
- They both represent the rate of change between two variables: In a proportional relationship, the unit rate and the slope both indicate how one variable changes in relation to the other. For example, if the unit rate is 3, it means that for every 1 unit increase in the independent variable, the dependent variable increases by 3 units.
- They both represent the constant of proportionality between two variables: The unit rate and the slope both represent the constant of proportionality. This means that they show the ratio between the two variables. For example, if the unit rate is 2, it means that the two variables are directly proportional, and for every 1 unit increase in the independent variable, the dependent variable increases by 2 units. The slope also represents the constant of proportionality, as it shows the ratio between the changes in the two variables.
- They both represent the steepness of the line on a graph: The unit rate and the slope both indicate the steepness of the line on a graph. A larger unit rate or slope means that the line is steeper, while a smaller unit rate or slope means that the line is less steep. This is because the unit rate and slope show the change in the dependent variable for a given change in the independent variable.