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Let's go through each problem:

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### Problem 4
**Function given:**  
\[
f(x) = \frac{5 - x}{3}
\]

This can be rewritten in slope-intercept form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. **Rewrite the function:**  
   Rewrite \( f(x) = \frac{5 - x}{3} \) by dividing each term in the numerator by 3:
   \[
   f(x) = -\frac{1}{3}x + \frac{5}{3}
   \]

2. **Identify the slope and y-intercept:**  
   - **Slope \( m \):** \(-\frac{1}{3}\)
   - **Y-intercept \( b \):** \(\frac{5}{3}\)

3. **Sketch the graph (conceptual):**  
   The graph is a line with a slope of \(-\frac{1}{3}\), meaning it decreases by \(\frac{1}{3}\) unit vertically for every 1 unit increase horizontally. It crosses the y-axis at \( y = \frac{5}{3} \).

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### Problem 5
**Goal:** Find \( f(x) \) if it is a linear function with the following properties:
1. **Slope = -5** and \( f\left(\frac{1}{4}\right) = 9 \)
2. \( f(-2) = 1 \) and \( f(-4) = -3 \)

Let's analyze each property to form the function \( f(x) \).

#### Approach for Part (i):
Since the slope \( m = -5 \), we can write the general form of \( f(x) \) as:
\[
f(x) = -5x + b
\]
where \( b \) is the y-intercept.

Using the condition \( f\left(\frac{1}{4}\right) = 9 \):
\[
f\left(\frac{1}{4}\right) = -5\left(\frac{1}{4}\right) + b = 9
\]
Solving this:
\[
-\frac{5}{4} + b = 9
\]
\[
b = 9 + \frac{5}{4} = \frac{36 + 5}{4} = \frac{41}{4}
\]
So, the function is:
\[
f(x) = -5x + \frac{41}{4}
\]

#### Approach for Part (ii):
Verify with the points \( f(-2) = 1 \) and \( f(-4) = -3 \) to confirm that this function is correct.

For \( f(-2) \):
\[
f(-2) = -5(-2) + \frac{41}{4} = 10 + \frac{41}{4} = \frac{40 + 41}{4} = \frac{81}{4} \neq 1
\]
There seems to be an inconsistency with this part. It appears these values may suggest a different function or could involve a constraint mismatch.

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Would you like further clarification on these solutions or to delve into why the values might not match in Problem 5 (ii)?

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### Follow-Up Questions:
1. How would you convert a linear function to slope-intercept form from different starting forms?
2. Why is it useful to know both the slope and y-intercept in graphing a linear function?
3. How does the slope affect the angle and direction of a line on the graph?
4. Can there be a linear function that satisfies two different pairs of points if the slope is set?
5. What does it mean if two points do not match a given slope in a linear context?

#### Tip:
In linear functions, always verify constraints by substituting back values; mismatched constraints may indicate no solution with the given slope.

4. Find the slope and vertical axis intercept of the following and sketch a graph: f(x) = (5 - x) / 3
5. Find f(x) if f is a linear function that has the given properties:
   i) Slope = -5, f(1/4) = 9
   ii) f(-2) = 1, f(-4) = -3

Solve for the slope and vertical axis intercept of f(x) = (5 - x) / 3 and determine the linear function with given slope and points. Explore algebraic methods to find y-intercepts and validate function properties for advanced high school students.

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