Describe a graph in which the function is y=x+2
The graph of the function y = x + 2 is a straight line with a slope of 1 and a y-intercept of 2.
Here is a step-by-step description of how this graph would look on a standard Cartesian coordinate system:
1. The y-intercept is the point on the graph where the line crosses the y-axis. For the function y = x + 2, the y-intercept is at the point (0, 2) because when x is 0, y is 2.
2. The slope of the line is the coefficient of x, which is 1 in this case. This means that for every unit increase in x, y increases by the same amount (1 unit). For example, if you were to start at the y-intercept (0, 2) and increase x by 1, you would move 1 unit right and 1 unit up to reach the point (1, 3). If you decrease x by 1 (moving left), you would also go down 1 unit to reach the point (-1, 1). This consistent behavior is what creates the straight line.
3. There are no curve or bends in the graph since this is a linear function, meaning it represents a constant rate of change.
4. Because the slope is positive, the line will continue to rise as it moves from the left to the right across the graph.
5. To graph this function, you would plot the y-intercept at point (0, 2), and from there, use the slope to find other points on the line. From (0, 2), you could go up 1 and right 1 to point (1, 3), then continue this pattern at other points, like (2, 4), (-1, 1), and so on. You can also move in the opposite direction by going down 1 and left 1 from the y-intercept to find additional points like (-2, 0).
6. After plotting a few points, draw a straight line through them, and make sure the line is extended in both directions, indicating that the function continues infinitely in both the positive and negative x directions.
In summary, the graph would show a straight line with an upwards tilt from left to right, crossing the y-axis at (0, 2), and continuing on indefinitely.