s the function represented by the table linear?

Question

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.

Answer 1

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 \( x \):

1. From \( x = 10 \) to \( x = 11 \):

   • Change in \( y = 1 - (-6) = 7 \)

2. From \( x = 11 \) to \( x = 12 \):

   • Change in \( y = 6 - 1 = 5 \)

3. 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.