show a graph that best represents a first-degree polynomial p(X).
Pick any such polynomial, find 2 points on it, the draw a line through those two points.
e.g.
P(x) = 3x + 1 or y = 3x+1
x = 1 ----> y = 4
x = 4 ----> y = 13
Try several of those.
To best represent a first-degree polynomial, also known as a linear function, you would need to plot a straight line on a graph. The standard form of a first-degree polynomial is:
p(x) = mx + b
Where m is the slope of the line, and b is the y-intercept. Here's how you can create a graph for a first-degree polynomial:
1. Choose a range for the x-values: Decide on a range of values for x that you want to plot on the graph. For example, you may choose x values from -10 to 10.
2. Determine the slope (m) and y-intercept (b): Depending on the given information or equation, identify the values of m and b. For example, if the equation is p(x) = 2x - 3, the slope is 2, and the y-intercept is -3.
3. Plot the y-intercept: On the graph, locate the y-axis (vertical axis) and mark the point where the line crosses it based on the y-intercept value. In this example, plot the point (0, -3).
4. Use the slope to find additional points: Based on the slope, find one or more additional points on the line. The slope represents the change in y divided by the change in x. For example, with a slope of 2, for every one unit increase in x, the y-value increases by 2. So, starting from the y-intercept (0, -3), move one unit to the right (increase x by 1) and two units up (increase y by 2). Plot this point (1, -1). Repeat this process to find more points if necessary.
5. Connect the points: Once you have plotted enough points, draw a straight line that passes through all the points. Make sure the line extends beyond the plotted points to represent the full range of x-values you chose.
Here is an example of a graph that represents the linear function p(x) = 2x - 3:
```
|
10 |
|
8 |
|
6 | x
| - - - - -
4 |
|
2 |
|
|_____________________
-10 -8 -6 -4 -2 0 2 4 6 8 10
```
In this graph, the line passes through the y-axis at -3 and has a slope of 2.