Determine the relationship between x and y.:
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Step 1 ：Observe the given table and notice that as x increases by 1, y increases by 4. This suggests a linear relationship between x and y.

Step 2 ：Calculate the slope of the line that these points would form on a graph. The slope is the change in y divided by the change in x. Use any two points to calculate this. For example, use the points (1,8) and (2,12). The change in y is $12-8=4$ and the change in x is $2-1=1$. So the slope is $4/1=4$. This means that for every increase of 1 in x, y increases by 4.

Step 3 ：Find the y-intercept by subtracting the product of the slope and the x-coordinate from the y-coordinate for any point. For example, use the point (1,8). The y-intercept is $8-4\ast 1=4$.

Step 4 ：Conclude that the relationship between x and y is given by the equation $y=4x+4$.

Step 5 ：Final Answer: $\boxed{{\displaystyle y=4x+4}}$