https://file.aiquickdraw.com/mathbot/file/1729623824261vwtvr1x3.jpg

Let's analyze the problem in the image.

1. **Function J** is given by the equation:
   \[
   y = \frac{3}{2}x - 4
   \]
   From this, we can determine that:
   - The **rate of change (slope)** is \( \frac{3}{2} \).
   - The **y-intercept** is \( -4 \).

2. **Function K** is represented in a table of values:
   \[
   \begin{array}{|c|c|}
   x & y \\
   \hline
   -1 & -6 \\
   -2 & -8 \\
   0 & -2 \\
   2 & 0 \\
   \end{array}
   \]
   To find the **rate of change (slope)** of Function K, we can use the slope formula between any two points \((x_1, y_1)\) and \((x_2, y_2)\):
   \[
   \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Let's calculate the slope between points \( (-1, -6) \) and \( (-2, -8) \):
   \[
   \text{slope of K} = \frac{-8 - (-6)}{-2 - (-1)} = \frac{-8 + 6}{-2 + 1} = \frac{-2}{-1} = 2
   \]
   So, the **rate of change for Function K** is 2.

   To find the **y-intercept** of Function K, observe that when \(x = 0\), \(y = -2\). Therefore, the **y-intercept** of Function K is \( -2 \).

---

### Now, let's compare the statements in the question:
- **The rate of change for Function J is equal to the rate of change for Function K.**
   - False. The rate of change of Function J is \( \frac{3}{2} \), and for Function K, it's 2.
   
- **The y-intercept of Function J is greater than the y-intercept of Function K.**
   - False. The y-intercept of Function J is \( -4 \), and the y-intercept of Function K is \( -2 \). Since \(-4\) is less than \(-2\), this statement is false.

- **The y-intercept of Function J is equal to the y-intercept of Function K.**
   - False. As mentioned, \( -4 \) is not equal to \( -2 \).

- **The rate of change for Function J is greater than the rate of change for Function K.**
   - False. \( \frac{3}{2} \approx 1.5 \), and 2 is greater than 1.5, so this statement is also false.

---

Therefore, none of the given answers seem to be correct based on the analysis. It appears that the selected answer is incorrect as well.

Would you like further clarification or details? 

Here are 5 related questions to deepen your understanding:
1. How would the graph of Function J compare to the graph of Function K based on their slopes?
2. What does the slope of a linear function represent in real-world applications?
3. How can you determine the equation of a line given two points on the line?
4. Why is the y-intercept important when graphing linear functions?
5. How would you graph both functions on the same coordinate plane?

**Tip:** The slope of a function determines how steep the line is. Comparing slopes helps you understand the relative steepness of two lines.

Robert has two linear functions as shown below:

Function J: y = (3/2)x - 4
Function K (given as a table of values)

Which statement about the functions is true?
- The rate of change for Function J is equal to the rate of change for Function K.
- The y-intercept of Function J is greater than the y-intercept of Function K.
- The y-intercept of Function J is equal to the y-intercept of Function K.
- The rate of change for Function J is greater than the rate of change for Function K.

Analyze and compare the slope and y-intercept of two linear functions, J and K. This problem covers key algebra concepts such as calculating slope from a table and interpreting y-intercepts. Suitable for students in Grades 7-9.

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