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Which tables display linear functions? Check all that apply. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1. Column 2 is labeled y with entries 1.5, 0, negative 1.5, negative 3. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries 0, negative 2, negative 1, negative 3. A 2-column table with 4 rows. Column 1 is labeled x with entries 4, 5, 6, 7. Column 2 is labeled y with entries negative 2.5, negative 5.5, negative 7.5, negative 10. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 4, negative 5, negative 6. Column 2 is labeled y with entries 6, 7, 8, 9.

User Dnang
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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.

User Dunken
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