Final answer:
In scientific experiments, the independent variable is manipulated to observe the effect on the dependent variable. Examples given include the age of drivers affecting the rate of fatalities and the number of family members influencing the weekly grocery bill. The slope and y-intercept in linear equations represent the rate of change and the starting point of the dependent variable, respectively.
Step-by-step explanation:
The independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable. The dependent variable is the variable being tested and measured in an experiment, and it is 'dependent' on the independent variable. As for the sentences provided:
- a. Age of drivers is the independent variable, and the number of fatalities per 100,000 drivers is the dependent variable.
- b. The number of family members is the independent variable, and the weekly grocery bill is the dependent variable.
- c. Age of the applicant is the independent variable, and life insurance premiums are the dependent variable.
- d. Power consumption is the independent variable, and utility bills are the dependent variable.
- e. The level of education is the independent variable, and the crime rate is the dependent variable.
In linear equations such as y = mx + b, the slope ('m') represents the rate of change of the dependent variable as the independent variable changes, while the y-intercept ('b') is the value of the dependent variable when the independent variable equals zero. In the context of Salk's nationwide polio vaccine trial, the independent variable could be the administration of the vaccine or a placebo, while the dependent variable would be the incidence of polio among the participants.