Question

A graph of an additive pattern contains the points (6,48)
and (10,52)
. What additive rule does the graph represent?(1 point)

Answer 1

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.

1. **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 \(52 - 48 = 4\).

2. **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.

3. **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:
\[
y = x + 42
\]