https://file.aiquickdraw.com/mathbot/file/17288662633902zv75888.jpg

We are given the function:

\[
f(x) = x - \frac{3 + 5x}{3}
\]

### Step 1: Simplifying the function
First, let's simplify the expression for \( f(x) \):

\[
f(x) = x - \frac{3 + 5x}{3}
\]

We can split the fraction:

\[
f(x) = x - \left(\frac{3}{3} + \frac{5x}{3}\right)
\]
\[
f(x) = x - 1 - \frac{5x}{3}
\]

Now, combine the terms involving \(x\):

\[
f(x) = \left(1x - \frac{5x}{3}\right) - 1
\]

We need a common denominator for \(x\):

\[
f(x) = \frac{3x}{3} - \frac{5x}{3} - 1
\]

Simplify:

\[
f(x) = \frac{-2x}{3} - 1
\]

### Step 2: Identifying the slope and y-intercept

This is now in the form of a linear equation \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

- The **slope** is \(m = \frac{-2}{3}\).
- The **y-intercept** occurs when \(x = 0\). Substituting \(x = 0\) into the simplified function:

\[
f(0) = \frac{-2(0)}{3} - 1 = -1
\]

So, the y-intercept is \((0, -1)\).

### Final Answer:
- **Slope:** \( \frac{-2}{3} \)
- **y-intercept:** \( (0, -1) \)

Let me know if you want further clarification! Here are some questions that expand on this concept:

1. How do you interpret the slope of a line in a real-world context?
2. What happens to the graph of the function if the slope changes to a positive value?
3. How can we find the x-intercept of this function?
4. What is the significance of the y-intercept in real-world problems?
5. How does the equation change if you add a constant to the function?

**Tip:** When simplifying linear functions, always try to express them in the form \(y = mx + b\) for easier identification of slope and intercepts.

Consider the function f(x) = x - (3 + 5x) / 3. Find the slope and the y-intercept. Express the intercept as an ordered pair. Simplify your answer.

Learn how to find the slope and y-intercept of the function f(x) = x - (3 + 5x) / 3. This problem simplifies the function and expresses it in slope-intercept form, covering algebraic concepts suitable for Grades 9-11.

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