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The task involves a linear relationship between variables \( j \) and \( k \). Let's break down the questions:

### Part a: 
The constant rate of change, \( \frac{\Delta k}{\Delta j} \), is given as \( -2.4 \). This means that for every increase of 1 unit in \( j \), \( k \) decreases by 2.4 units.

### Part b: 
We need to fill in the missing values in the table. The linear formula for \( k \) with respect to \( j \) can be written as:

\[
k = m \cdot j + b
\]

where \( m \) is the slope (\( -2.4 \)) and \( b \) is the y-intercept (we need to find this). Using a known point like \( j = -7 \) and \( k = 10.8 \), we can find \( b \):

\[
10.8 = -2.4(-7) + b
\]

Solving for \( b \):

\[
10.8 = 16.8 + b
\]
\[
b = 10.8 - 16.8 = -6
\]

Now the equation for the line is:

\[
k = -2.4j - 6
\]

Using this equation, we can fill in the missing values:

1. For \( j = -2 \):
   \[
   k = -2.4(-2) - 6 = 4.8 - 6 = -1.2
   \]

2. For \( j = 6 \):
   \[
   k = -2.4(6) - 6 = -14.4 - 6 = -20.4
   \]

So, the missing values in the table are:
- \( j = -2 \), \( k = -1.2 \) (already filled)
- \( j = 6 \), \( k = -20.4 \)

### Part c:
The formula for \( k \) in terms of \( j \) is:

\[
k = -2.4j - 6
\]

This formula should be entered into the appropriate box.

Would you like any further details or have any questions about this explanation? Here are 5 related questions to expand your understanding:

1. How do you interpret the meaning of a negative slope in a linear equation?
2. How would you find the y-intercept using another point from the table?
3. Can you graph the linear function to visualize the relationship between \( j \) and \( k \)?
4. What happens to the value of \( k \) as \( j \) becomes increasingly positive?
5. Can you explain how to use the slope to determine the change in \( k \) for different values of \( j \)?

**Tip:** Always use known points to help solve for unknown values in linear equations.

A linear relationship exists between the quantities j and k. Determine the constant rate of change (already given as -2.4), fill in the missing values, and write the formula representing the value of k with respect to j.

Solve a linear relationship problem involving variables j and k. Calculate the missing values in the table, determine the rate of change, and find the formula representing k in terms of j using the slope-intercept form. Suitable for high school algebra students.

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