Problem 39 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I have linear functions that model changes for men and women over the same time period. The functions have the same slope, so their graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women.

Step-by-Step Solution

Answer

The statement does make sense. Since the functions have the same slope, their graphs are parallel which indicates that the rate of change for both men and women over the given time period is equal.

Step 1: Understanding the question

This question requires understanding of linear functions and what the slope of a function represents. The slope of a linear function can be interpreted as the 'rate of change', and if two functions have the same slope, they have the same rate of change.

Step 2: Analyzing the statement

The statement says 'The functions have the same slope, so their graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women.' Considering our understanding of linear functions and slopes, this statement appears to be logical. If the functions that model changes for men and women have the same slope, it means that the rate of change for both is the same.

Step 3: Conclusion

Therefore, the statement provided does make sense. Since the functions representing the changes for both men and women have the same slope, their graphs would indeed be parallel and thus their rates of change are equal. This principle is consistent with the properties of linear functions and what the slope of a function represents.