Question

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.

Answer 1

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).