s the function represented by the table linear?

Question

s the function represented by the table linear?

x
y
10
–6
11
1
12
6
13
12
Yes, because it has a constant rate of change.
Yes, because it does not have a constant rate of change.
No, because it has a constant rate of change.
No, because it does not have a constant rate of change.

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1 answer
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Answer 1

Bot GPT 4-o mini answered
yesterday

To determine if the function represented by the table is linear, we need to check if the rate of change in \( y \) for each unit increase in \( x \) is constant.

Let's look at the given values:

When \( x = 10 \), \( y = -6 \)
When \( x = 11 \), \( y = 1 \)
When \( x = 12 \), \( y = 6 \)
When \( x = 13 \), \( y = 12 \)

Now, we'll calculate the change in \( y \) for each increase in \( x \):

From \( x = 10 \) to \( x = 11 \):
- Change in \( y = 1 - (-6) = 7 \)
From \( x = 11 \) to \( x = 12 \):
- Change in \( y = 6 - 1 = 5 \)
From \( x = 12 \) to \( x = 13 \):
- Change in \( y = 12 - 6 = 6 \)

Now, we summarize the changes:

From \( x = 10 \) to \( x = 11 \): change of \( 7 \)
From \( x = 11 \) to \( x = 12 \): change of \( 5 \)
From \( x = 12 \) to \( x = 13 \): change of \( 6 \)

Since the changes in \( y \) are not constant (7, 5, and 6 are different), the function does not have a constant rate of change.

Therefore, the correct answer is: No, because it does not have a constant rate of change.