To find the equation that represents the relationship between $x$ and $y$, we can analyze the given data points in the table.

The table provides the following pairs of $(x, y)$ values:
- $(8, 12)$
- $(10, 14)$
- $(11, 15)$
- $(12.50, 16.50)$
- $(14, 18)$

Let's look for a linear relationship of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

First, let's find the slope $m$ using the first two points $(8, 12)$ and $(10, 14)$:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 12}{10 - 8} = \frac{2}{2} = 1$

Now that we have the slope $m = 1$, we can use one of the points to find the y-intercept $b$. Let's use the point $(8, 12)$:
$12 = 1(8) + b$
$12 = 8 + b$
$b = 12 - 8 = 4$

So the equation is $y = 1x + 4$, which simplifies to $y = x + 4$.

Let's check if this equation holds for the other points:
- For $(11, 15)$: $15 = 11 + 4 = 15$ (True)
- For $(12.50, 16.50)$: $16.50 = 12.50 + 4 = 16.50$ (True)
- For $(14, 18)$: $18 = 14 + 4 = 18$ (True)

Since the equation $y = x + 4$ holds true for all the given points, it represents the relationship between $x$ and $y$.

Final Answer: The final answer is $\boxed{y=x+4}$

To find the equation that represents the relationship between $x$ and $y$ for the given data points in the table, we can follow a similar approach as before.

The table provides the following pairs of $(x, y)$ values:
- $(-5, -8)$
- $(-4, -7)$
- $(-3, -6)$
- $(-2, -5)$
- $(-1, -4)$

Let's look for a linear relationship of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

First, let's find the slope $m$ using the first two points $(-5, -8)$ and $(-4, -7)$:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-8)}{-4 - (-5)} = \frac{-7 + 8}{-4 + 5} = \frac{1}{1} = 1$

Now that we have the slope $m = 1$, we can use one of the points to find the y-intercept $b$. Let's use the point $(-5, -8)$:
$-8 = 1(-5) + b$
$-8 = -5 + b$
$b = -8 + 5 = -3$

So the equation is $y = 1x - 3$, which simplifies to $y = x - 3$.

Let's check if this equation holds for the other points:
- For $(-4, -7)$: $-7 = -4 - 3 = -7$ (True)
- For $(-3, -6)$: $-6 = -3 - 3 = -6$ (True)
- For $(-2, -5)$: $-5 = -2 - 3 = -5$ (True)
- For $(-1, -4)$: $-4 = -1 - 3 = -4$ (True)

Since the equation $y = x - 3$ holds true for all the given points, it represents the relationship between $x$ and $y$.

Final Answer: The final answer is $\boxed{y=x-3}$