Alright, let's break this down in an easy and step-by-step way. To determine if a table displays a linear function, we need to check if the change in y-values (vertical) is consistent for each change in x-values (horizontal). This consistent change is often referred to as the slope in algebra, and for a function to be linear, the slope must remain constant.
Let's go through each table:
1. Table 1:
- Column 1 (x): -2, -1, 0, 1
- Column 2 (y): 1.5, 0, -1.5, -3
For every step of +1 in x (from -2 to -1 to 0 to 1), y decreases by 1.5 (from 1.5 to 0 to -1.5 to -3). This change is consistent, so the slope is constant.
Verdict: Table 1 displays a linear function.
2. Table 2:
- Column 1 (x): -1, 0, 1, 2
- Column 2 (y): 0, -2, -1, -3
For the first step in x (+1 from -1 to 0), y decreases by 2. However, for the next step in x (+1 from 0 to 1), y increases by 1. This shows that the change in y is not consistent for the same change in x.
Verdict: Table 2 does not display a linear function.
3. Table 3:
- Column 1 (x): 4, 5, 6, 7
- Column 2 (y): -2.5, -5.5, -8.5, -11.5
For every step of +1 in x (from 4 to 5 to 6 to 7), y decreases by 3 (from -2.5 to -5.5 to -8.5 to -11.5). This change is consistent, so the slope is constant.
Verdict: Table 3 displays a linear function.
4. Table 4:
- Column 1 (x): -3, -4, -5, -6
- Column 2 (y): 6, 7, 8, 9
For every step of -1 in x (from -3 to -4 to -5 to -6), y increases by 1 (from 6 to 7 to 8 to 9). This change is consistent, so the slope is constant.
Verdict: Table 4 displays a linear function.
To sum it up, Tables 1, 3, and 4 display linear functions, while Table 2 does not.