Which tables of values represent linear functions?
Select 2 choice(s)
x ‒1 0 1 2
y ‒2.5 ‒3 ‒3.5 ‒4
x ‒1 0 1 2
y 3 5 7 9
x ‒1 0 1 2
y 2 ‒2 2 ‒2
x ‒2 0 2 4
y ‒5 0 10 20
x ‒1 0 1 2
y ‒0.5 0 ‒0.5 ‒2

To determine which tables of values represent linear functions, we need to check whether the differences in \( y \)-values are consistent for equal differences in \( x \)-values. A linear function will have a constant rate of change, meaning the difference between consecutive \( y \)-values divided by the difference between consecutive \( x \)-values will always be the same.

Let's check each option:

### Option 1:
\[
\begin{aligned}
x: &\quad -1, 0, 1, 2 \\
y: &\quad -2.5, -3, -3.5, -4 \\
\end{aligned}
\]
- Change in \( x \): \( 1 - (-1) = 1 \)
- Change in \( y \): \( -3 - (-2.5) = -0.5 \), \( -3.5 - (-3) = -0.5 \), \( -4 - (-3.5) = -0.5 \)

Since the change in \( y \) is constant, this table represents a **linear function**.

### Option 2:
\[
\begin{aligned}
x: &\quad -1, 0, 1, 2 \\
y: &\quad 3, 5, 7, 9 \\
\end{aligned}
\]
- Change in \( x \): \( 1 - (-1) = 1 \)
- Change in \( y \): \( 5 - 3 = 2 \), \( 7 - 5 = 2 \), \( 9 - 7 = 2 \)

The change in \( y \) is constant, so this also represents a **linear function**.

### Option 3:
\[
\begin{aligned}
x: &\quad -1, 0, 1, 2 \\
y: &\quad 2, -2, 2, -2 \\
\end{aligned}
\]
The \( y \)-values alternate between 2 and -2, which means the differences are not constant, so this is **not a linear function**.

### Option 4:
\[
\begin{aligned}
x: &\quad -2, 0, 2, 4 \\
y: &\quad -5, 0, 10, 20 \\
\end{aligned}
\]
- Change in \( x \): \( 2 - (-2) = 4 \)
- Change in \( y \): \( 0 - (-5) = 5 \), \( 10 - 0 = 10 \), \( 20 - 10 = 10 \)

The rate of change is not constant, so this is **not a linear function**.

### Option 5:
\[
\begin{aligned}
x: &\quad -1, 0, 1, 2 \\
y: &\quad -0.5, 0, -0.5, -2 \\
\end{aligned}
\]
The differences in \( y \)-values are inconsistent, so this is **not a linear function**.

### Conclusion:
The tables representing linear functions are **Option 1** and **Option 2**.

Would you like more details or have any questions?  
Here are some follow-up questions:

1. How can you determine a linear function from an equation?
2. What are the characteristics of a non-linear function?
3. How do you find the slope from a table of values?
4. Can a linear function have a negative slope?
5. What real-life situations can be modeled by linear functions?

**Tip:** To quickly identify a linear function, look for a constant rate of change in the \( y \)-values relative to the \( x \)-values.

Which tables of values represent linear functions? Select 2 choice(s) x ‒1 0 1 2 y ‒2.5 ‒3 ‒3.5 ‒4 x ‒1 0 1 2 y 3 5 7 9 x ‒1 0 1 2 y 2 ‒2 2 ‒2 x ‒2 0 2 4 y ‒5 0 10 20 x ‒1 0 1 2 y ‒0.5 0 ‒0.5 ‒2

Learn how to identify linear functions from tables of values. This problem focuses on recognizing consistent rates of change, using key concepts such as the rate of change formula and linear functions. Suitable for Grades 7-9 students.

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