https://file.aiquickdraw.com/mathbot/file/172909493290947tbdx34.jpg

To solve the problem, we need to determine two things for the linear function:

1. **The rate of change (slope)**
2. **The initial value (y-intercept)**

### 1. Calculating the Rate of Change (Slope)
The rate of change (slope) of a linear function is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

From the problem, we are given:
- Point \(E(0, 27)\)
- Point \(F(5, -8)\)

So,
\[
m = \frac{-8 - 27}{5 - 0} = \frac{-35}{5} = -7
\]
The rate of change (slope) is \(-7\).

### 2. Initial Value (y-intercept)
The initial value is the value of \(y\) when \(x = 0\). From point \(E(0, 27)\), we can directly see that the initial value is \(27\).

### Final Answer:
- The rate of change for the linear function is **\(-7\)**.
- The initial value is **27**.

Would you like more details or further clarification? Here are a few related questions to consider:

1. How do you interpret the slope of a linear function in real-world scenarios?
2. How can you use the slope-intercept form of a line equation to predict values?
3. What does it mean if the slope is negative, as in this case?
4. How would the graph of this linear function look?
5. How can we check if other points lie on the same line?

**Tip:** The y-intercept is always found where the line crosses the y-axis (i.e., when \(x = 0\)).

A relation is plotted as a linear function on the coordinate plane starting at point E(0, 27) and ending at point F(5, -8). What is the rate of change for the linear function and what is its initial value?

Determine the rate of change (slope) and initial value (y-intercept) for a linear function passing through points E(0, 27) and F(5, -8). This math problem involves using the slope formula and understanding basic linear functions, suitable for students in Grades 8-10.

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