Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer.
Linear Function 1: y = 2x - 3
Linear Function 2: y = -x + 5
| x | y1=2x-3 | y2=-x+5 |
|-------|-------------|-------------|
| 0 | -3 | 5 |
| 1 | -1 | 4 |
| 2 | 1 | 3 |
| 3 | 3 | 2 |
| 4 | 5 | 1 |
Based on the table, the graphs of these two linear functions will intersect. This can be determined by observing that as x increases, the values of y for the first function (y1=2x-3) also increase, and conversely, the values of y for the second function (y2=-x+5) decrease. The point at which the two functions intersect is when their respective y-values are equal, which in this case occurs when x = 2 and y = 1. Therefore, the graphs of these two functions will intersect at the point (2, 1).
Sure! Let's create a table of data for two different linear functions.
Let's consider two linear functions:
Function 1: f(x) = 2x + 3
Function 2: g(x) = -3x + 7
Let's choose some values of x and calculate the corresponding values of y for each function. We'll use the same values of x for both functions.
Table of Data:
| x | f(x) | g(x) |
-------------------------------
| -2 | -1 | 13 |
| 0 | 3 | 7 |
| 2 | 7 | 1 |
| 4 | 11 | -5 |
Now, let's plot the points on a graph to see if the graphs of these two functions intersect:
Graph:
```
|
13 | g(x)
| .
| .
7 | . . . . . . . . .
| .
| .
1 | . . . . . . . . . . .
|
-5 | . . . . . . . . . . . .
----------------------
-2 0 2 4
```
As we can see from the graph and the table of data, the graphs of these two linear functions do intersect at the point (2, 7). Therefore, the answer is yes, the graphs of these two functions intersect.
Is there anything else that you would like to know?
To create a table of data for two different linear functions, we need to define the functions first. A linear function can be represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
Let's assume the first linear function as f(x) = 2x + 3, and the second linear function as g(x) = -3x + 7.
To create a table of data, we will choose a few values for x and calculate the corresponding y-values for each function.
Let's choose the values of x as -2, 0, and 2:
For the first function (f(x) = 2x + 3):
When x = -2: f(-2) = 2(-2) + 3 = -4 + 3 = -1
When x = 0: f(0) = 2(0) + 3 = 0 + 3 = 3
When x = 2: f(2) = 2(2) + 3 = 4 + 3 = 7
For the second function (g(x) = -3x + 7):
When x = -2: g(-2) = -3(-2) + 7 = 6 + 7 = 13
When x = 0: g(0) = -3(0) + 7 = 0 + 7 = 7
When x = 2: g(2) = -3(2) + 7 = -6 + 7 = 1
Now, let's create a table to organize this data:
x | f(x) = 2x + 3 | g(x) = -3x + 7
-------------------------------------
-2 | -1 | 13
0 | 3 | 7
2 | 7 | 1
To determine whether the graphs of these two functions intersect, we need to check if there is any common point (x, y) in the table for both functions. In this case, we can observe that the two functions intersect at the point (2, 7).
So, based on the data in the table, we can conclude that the graphs of these two linear functions will intersect at (2, 7).