To find the linear equation that represents the relationship between $x$ and $y$ in the table, we can observe that as $x$ increases by 1, $y$ also increases by 1. This suggests that the slope of the line is 1. We can write the equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Given that the slope $m = 1$, we can use one of the points to find $b$. Let's use the point $(5, 83)$:

$y = mx + b$ $83 = 1(5) + b$ $83 = 5 + b$ $b = 83 - 5 = 78$

Thus, the equation that represents the relationship between $x$ and $y$ is:

$y = x + 78$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the slope of the equation $y = 2x + 3$?
2. How do you find the y-intercept of a linear equation?
3. What is the equation of a line with slope 2 passing through the point $(1, 4)$?
4. How can you tell if a table of values represents a linear relationship?
5. If a linear equation has a slope of 0, what does its graph look like?

Tip: The slope of a line represents how much the y-value changes for every 1 unit increase in the x-value.