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.

Question

Use this example as a reference...
4x + 5 x | y ------ 4 | 4(4) + 5 = 21 6 | 4(6) + 5 = 29 8 | 4(8) + 5 = 37 2x + 3 x | y ----- 2 | 2(2) + 3 = 7 4 | 2(4) + 3 = 11 6 | 2(6) + 3 = 15 I think the graph will intersect at (-1 -1) since if you graph the two functions and draw a line down each of the points, they eventually intersect there.

Answer 1

Here are two different linear functions:

Function 1: y = 3x + 2
Function 2: y = -2x + 6

Let's create a table using the same values of x for both functions.

x | Function 1 | Function 2
---------------------------
1 | 5 | 4
2 | 8 | 2
3 | 11 | 0
4 | 14 | -2
5 | 17 | -4

Based on this table, the graphs of these two functions will intersect. As we can see, the y-values for both functions are different for each corresponding x-value. Therefore, the graphs of these functions will cross or intersect at some point.