Table of x and y values representing a linear relationship.

Let’s look at the table and see if we can find a pattern between x and y.

We have these pairs:
- When x = -2, y = -7
- When x = -1, y = -4
- When x = 0, y = -1
- When x = 1, y = 2
- When x = 2, y = 5

Let’s check how much y changes when x increases by 1.

From x = -2 to x = -1 → y goes from -7 to -4 → that’s +3
From x = -1 to x = 0 → y goes from -4 to -1 → that’s +3
From x = 0 to x = 1 → y goes from -1 to 2 → that’s +3
From x = 1 to x = 2 → y goes from 2 to 5 → that’s +3

So every time x increases by 1, y increases by 3. That means the relationship is linear, and the slope (rate of change) is 3.

Now, let’s find the equation in the form:
y = mx + b

We know m = 3.

Now plug in one point to find b. Let’s use (0, -1) — because when x=0, it’s easy.

y = 3x + b
-1 = 3(0) + b
→ b = -1

So the equation is:
y = 3x - 1

Let’s test it with another point to be sure.

Try x = 1:
y = 3(1) - 1 = 2 ✔ matches the table

Try x = -2:
y = 3(-2) - 1 = -6 -1 = -7 ✔ matches

Try x = 2:
y = 3(2) - 1 = 6 - 1 = 5 ✔ matches

Perfect! The rule is consistent.

Final Answer:
y = 3x - 1