How are the functions \( y=x \) and \( y=x-5 \) related? How are their graphs related? Each output for \( y=x-5 \) is 5 more than the corresponding output for \( y=x \). The graph of \( y=x-5 \) is the graph of \( y=x \) translated down 5 units. Each output for \( y=x-5 \) is 5 less than the corresponding output for \( y=x \). The graph of \( y=x-5 \) is the graph of \( y=x \) translated up 5 units. Each output for \( y=x-5 \) is 5 less than the corresponding output for \( y=x \). The graph of \( y=x-5 \) is the graph of \( y=x \) translated down 5 units. Each output for \( y=x-5 \) is 5 more than the corresponding output for \( y=x \) The graph of \( y=x-5 \) is the graph of \( y=x \) translated up 5 units.

To analyze the relationship between the functions \( y = x \) and \( y = x - 5 \), let's break it down: 1. **Output Relationship**: - For the function \( y = x \), the output is simply the value of \( x \). - For the function \( y = x - 5 \), the output is the value of \( x \) minus 5. - Therefore, for any given \( x \), the output of \( y = x - 5 \) is 5 less than the output of \( y = x \). This means: \[ y = x - 5 \quad \text{is 5 less than} \quad y = x. \] 2. **Graph Relationship**: - The graph of \( y = x \) is a straight line that passes through the origin (0,0) with a slope of 1. - The graph of \( y = x - 5 \) is also a straight line with the same slope of 1, but it is shifted down by 5 units. This means that every point on the graph of \( y = x \) is translated down 5 units to get the corresponding point on the graph of \( y = x - 5 \). Based on this analysis, the correct statements are: - Each output for \( y = x - 5 \) is 5 less than the corresponding output for \( y = x \). - The graph of \( y = x - 5 \) is the graph of \( y = x \) translated down 5 units. Thus, the correct answer is: - Each output for \( y=x-5 \) is 5 less than the corresponding output for \( y=x \). - The graph of \( y=x-5 \) is the graph of \( y=x \) translated down 5 units.