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To answer the questions in this table, we first need to analyze the rate of change and y-intercept for **Function H** and **Function J**.

### Step 1: Determine the rate of change and y-intercept of Function H
Looking at the table for Function \( H \), we have pairs \((x, y)\) values:  
\[
(-4, -18), (-2, -10), (0, -2), (2, 6)
\]

#### Rate of Change (Slope) for Function H
The slope (rate of change) of a linear function can be calculated by the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-4, -18)\) and \((-2, -10)\):
\[
\text{slope} = \frac{-10 - (-18)}{-2 - (-4)} = \frac{8}{2} = 4
\]
So, the rate of change for Function \( H \) is \( 4 \).

#### Y-Intercept of Function H
The y-intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = -2 \), so the y-intercept for Function \( H \) is \( -2 \).

### Step 2: Compare with Function J
The equation for Function \( J \) is:
\[
f(x) = \frac{1}{4}x - 2
\]
Here:
- The slope (rate of change) is \( \frac{1}{4} \).
- The y-intercept is \( -2 \).

### Step 3: Evaluate Each Statement
Now, we can answer each statement based on these values.

1. **The rate of change for Function H is less than the rate of change for Function J.**
   - **False**, because the rate of change for \( H \) (4) is greater than that of \( J \) \((\frac{1}{4})\).

2. **The rate of change for Function H is equal to the rate of change of Function J.**
   - **False**, because the rate of change for \( H \) (4) is not equal to the rate of change of \( J \) \((\frac{1}{4})\).

3. **The y-intercept of Function H is equal to the y-intercept of Function J.**
   - **True**, because both \( H \) and \( J \) have a y-intercept of \( -2 \).

4. **The y-intercept of Function H is greater than the y-intercept of Function J.**
   - **False**, because both y-intercepts are the same at \( -2 \), so neither is greater.

### Summary of Answers
- **First statement**: False
- **Second statement**: False
- **Third statement**: True
- **Fourth statement**: False

Would you like further explanation on any part of this solution? 

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### Related Questions
1. What is the significance of the rate of change in a linear function?
2. How does the y-intercept impact the graph of a linear function?
3. Can two different functions have the same rate of change but different y-intercepts?
4. How would you calculate the slope if only one point is given?
5. What does it mean if two functions have the same rate of change but different y-intercepts?

### Tip
For linear functions, if the slopes (rates of change) differ, the lines are not parallel and will intersect at some point unless they are on the same line.

Identify each of the following statements as either True or False based on the given table of values for Function H and the equation for Function J: f(x) = (1/4)x - 2.

Analyze and determine the truth of statements related to rate of change and y-intercepts for two linear functions. This problem involves calculating slope, comparing y-intercepts, and applying the slope-intercept form to functions H and J. Suitable for students in Grades 8-10.

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