Describe how the graphs of y = |x| and y = |x| – 15 are related.
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.
To understand how the graphs of y = |x| and y = |x| - 15 are related, we can first analyze each equation separately.
The equation y = |x| represents the absolute value function. It produces a graph that is a V-shape, symmetric with respect to the y-axis. The y-intercept of y = |x| is 0, meaning that the point (0, 0) lies on the graph.
Now, let's consider the equation y = |x| - 15. This equation is similar to the first one but with an additional constant, which produces a vertical shift downward. By subtracting 15 from the absolute value of x, the entire graph is shifted vertically downward by 15 units. This shift changes the y-intercept of the graph from 0 to -15, meaning that the point (0, -15) lies on the graph.
Therefore, the correct answer is: The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is -15.