Explanation:
The given function is y = x - 4. Let's plot the points on the graph.
x | y
3 | -1
-3 | -7
-2 | -6
0 | -4
-1 | -5
1 | -3
2 | -2
When we plot these points, we get a straight line with a slope of 1 passing through the point (0, -4). The line goes up as x increases.
Now, let's compare this graph to the function y = x. The function y = x represents a straight line with a slope of 1 passing through the origin (0, 0). It has a positive slope, meaning the line goes up as x increases.
The key difference between the two graphs is the vertical shift. In the graph of y = x - 4, the line is shifted downward by 4 units compared to the line of y = x. The slope and the direction of the line remain the same.
Now, let's make a prediction about the function y = x + 7.
Since this function has a slope of 1, just like y = x and y = x - 4, the graph of y = x + 7 would also be a straight line. However, the graph would be shifted vertically upwards by 7 units. The line would still have a positive slope and pass through the point (0, 7) instead of the origin (0, 0).
In summary, the graph of y = x - 4 is a straight line with a downward shift of 4 units compared to y = x. If we graph the function y = x + 7, it would also be a straight line but shifted upwards by 7 units.
I hope this helps! Let me know if you have any further questions.