How are the functions y=x and y=x-3 related ho are their graphs related
The functions y=x and y=x-3 are related because one can be obtained from the other by subtracting 3 from both sides.
Their graphs are also related because they are both straight lines. The graph of y=x is a line that passes through the origin (0,0) with a slope of 1. The graph of y=x-3 is also a straight line, but it is shifted downward by 3 units compared to the graph of y=x. Both lines have the same slope of 1.
The functions y=x and y=x-3 are related because the second function is derived from the first by subtracting 3 from the y-coordinate. In other words, the function y=x-3 is a shifted version of the function y=x.
As for their graphs, both functions represent straight lines. The graph of y=x is a diagonal line that passes through the origin (0,0) with a slope of 1. On the other hand, the graph of y=x-3 is also a straight line, but it is shifted downward by 3 units compared to the graph of y=x. This means that every point on the graph of y=x-3 is 3 units lower than the corresponding point on the graph of y=x.
In conclusion, the relationship between the functions y=x and y=x-3 is that the latter is obtained by shifting the former downward by 3 units. This shift is reflected in their respective graphs as well.
The functions y=x and y=x-3 are related as follows:
1. Relationship in terms of Equations:
- The equation y=x represents a linear function where the value of y is equal to the value of x. This means that for any given x-coordinate, the y-coordinate will be the same.
- The equation y=x-3 represents another linear function, but with a slight modification. Here, the value of y is equal to the value of x minus 3. So, for any given x-coordinate, the y-coordinate will be three units less.
2. Relationship in terms of Graphs:
- The graph of y=x is a straight line with a slope of 1, passing through the origin (0,0). It has a positive slope, which means it slants upwards from left to right.
- On the other hand, the graph of y=x-3 is also a straight line but shifted downwards by three units compared to the graph of y=x. It has the same slope of 1 but crosses the y-axis three units below the origin.
In summary, the functions y=x and y=x-3 are related in that they have the same slope but differ by a vertical shift of three units downwards in their respective graphs.