Describe how the graphs of y = |x| and y = |x| – 15 are related. (1 point) Responses The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15. The graphs have the same shape. The y -intercept of y = | x | is 0, and the x -intercept of the second graph is –15. The graphs have the same y-intercept. The second graph is steeper than y = |x|. The graphs have the same y -intercept. The second graph is steeper than y = | x |. The two graphs are the same. The two graphs are the same. The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.
The correct response is: The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15.
The correct response is:
The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15.
To describe the relationship between the graphs of y = |x| and y = |x| – 15, we need to analyze their key features.
Firstly, let's focus on the shape of the graphs. Both y = |x| and y = |x| – 15 consists of two sections, one increasing and one decreasing, which creates a "V" shape. Therefore, the statement "The graphs have the same shape" is correct.
Now, let's consider the y-intercept of y = |x|, which refers to the point where the graph intersects the y-axis. In this case, the y-intercept is at the origin, (0,0), since the absolute value of any number is zero when the number itself is zero. Moving on to the second graph, y = |x| – 15, we analyze its x-intercept, which is the point where the graph intersects the x-axis. The x-intercept in this case is -15, as setting y to zero gives us |x| – 15 = 0, and solving for x results in x = -15. Thus, the statement "The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15" is accurate.
Comparing the steepness of the graphs, we can observe that the second graph, y = |x| – 15, is steeper than y = |x|. This means that the slope of the second graph is larger, indicating a faster rate of change. Consequently, the statement "The second graph is steeper than y = |x|" is correct.
Summarizing the information, the accurate description of the relationship between the two graphs is: "The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15. The second graph is steeper than y = |x|."