Describe how the graphs of y =IXI nand ym = IXI -15 are related.
1- the graphs have the same shape,. The y intercept of the 2nd graph is -15
2-the graphs have the same y intercept. The 2nd graph is steeper than y= absolute x
3- the 2 graphs are the same
4- the graphs have the same Shape. the y intercept of y =m absolute x is 0 and the y intercept of the second graph is -15
The answer is 4
The correct answer is: 4- the graphs have the same shape. The y-intercept of y = m|X| is 0, and the y-intercept of the second graph y = |X| - 15 is -15.
To compare the graphs of y = |x| and y = |x| - 15, we can start by understanding the individual equations and then analyzing their respective graphs.
1. y = |x|
This equation represents the absolute value function, which means that the output (y) will always be positive or zero. The graph of y = |x| consists of a V-shape, with the vertex at the origin (0, 0). It is symmetric with respect to the y-axis.
2. y = |x| - 15
In this equation, the constant value of 15 is subtracted from the absolute value function. This vertically shifts the graph downward by 15 units. The vertex of the V-shape is now located at (0, -15), which is the y-intercept of the graph.
Now, let us consider the given options:
1. The graphs have the same shape, but the y-intercept of the second graph is -15.
This option is correct. Both graphs are V-shaped and have the same shape. However, the second graph y = |x| - 15 is vertically shifted downwards, resulting in a y-intercept of -15.
2. The graphs have the same y-intercept. The second graph is steeper than y = |x|.
This option is not correct. While the y-intercept of both graphs is different, the steepness of the two graphs remains the same. The coefficient of x in both equations is 1, indicating that there is no change in the slope or steepness.
3. The two graphs are the same.
This option is not correct. The two graphs are not identical because they have different y-intercepts. Even though they have the same shape, the vertical shift causes them to have distinct positions.
4. The graphs have the same shape, but the y-intercept of y = m|x| is 0, and the y-intercept of the second graph is -15.
This option is correct. The shape of the graphs remains the same, and the y-intercept of the first graph y = |x| is indeed 0. The y-intercept of the second graph is, as mentioned earlier, -15 due to the vertical shift.
Therefore, the correct answer is: Option 4 - The graphs have the same shape. The y-intercept of y = m|x| is 0, and the y-intercept of the second graph is -15.