To find the additive rule from the given points (6, 48) and (10, 52), we can analyze how the output changes as the input increases.
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Identify the change in x and y:
- The change in x from 6 to 10 is \(10 - 6 = 4\).
- The change in y from 48 to 52 is \(52 - 48 = 4\).
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Determine the additive relationship: This means that for every increase of 4 in x, y increases by 4 as well. This indicates a constant additive pattern where each increase in x leads to an equal increase in y.
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Finding the additive rule: We can set up an expression based on the points. One way to express the relationship is: \[ y = x + k \] where \(k\) is a constant that we will determine using one of the points.
Let's use the point (6, 48): \[ 48 = 6 + k \implies k = 48 - 6 = 42 \]
Now let's verify with the second point (10, 52): \[ 52 = 10 + 42 \implies 52 = 52 \] This is correct.
Therefore, the additive rule represented by the graph is: \[ y = x + 42 \]
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