To solve this matching problem, we need to identify the correct equation for each table of values. Let's break down the process:

1. First Table:

   • $x = 0, 1, 2, 3$
   • $y = -4, -1, 2, 5$

   This set shows that when $x$ increases by 1, $y$ increases by 3. This suggests a slope of 3, and the equation is likely of the form $y = 3x + b$. Let's check:

   • $y = 3(0) - 4 = -4$ So the equation matches $y = 3x - 4$.

2. Second Table:

   • $x = -2, 0, 2, 4$
   • $y = 10, 4, -2, -8$

   The change in $y$ when $x$ increases by 2 is consistently $-6$, indicating a slope of $-3$. The equation is $y = -3x + 4$. Checking values confirms this.

3. Third Table:

   • $x = 3, 6, 9, 12$
   • $y = 3, 2, 1, 0$

   As $x$ increases, $y$ decreases by 1 for every increase of 3 in $x$, indicating a slope of $-\frac{1}{3}$. The equation is likely $y = -\frac{1}{3}x + 4$.

4. Fourth Table:

   • $x = -12, -6, 6, 12$
   • $y = -8, -6, -2, 0$

   The values suggest a positive slope of $\frac{1}{3}$. The equation is $y = \frac{1}{3}x - 4$.

Now, matching the tables to the equations:

• First table (top): $y = 3x - 4$
• Second table: $y = -3x + 4$
• Third table: $y = -\frac{1}{3}x + 4$
• Fourth table (bottom): $y = \frac{1}{3}x - 4$

Do you want more details on how these equations are derived, or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the process for calculating the slope between two points?
2. How do you determine the y-intercept from a table of values?
3. What are the differences between positive and negative slopes in graphs?
4. Can a linear equation have a fractional slope, and what does that represent?
5. How do you check if a point lies on a given line?

Tip: Always check the consistency of the slope across all points in the table when determining linear relationships!