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The given function is \( y = \frac{1}{5}x - \frac{2}{3} \).

We need to verify which of the sets of ordered pairs corresponds to points on the graph of this function. To do that, we will substitute the \( x \)-coordinates of the points into the function and check if the resulting \( y \)-values match those given in each option.

Let's start by evaluating the function for different values of \( x \):

1. **For \( x = -1 \):**
   \[
   y = \frac{1}{5}(-1) - \frac{2}{3} = -\frac{1}{5} - \frac{2}{3} = -\frac{3}{15} - \frac{10}{15} = -\frac{13}{15}
   \]
   So, \( y = -\frac{13}{15} \).

2. **For \( x = 0 \):**
   \[
   y = \frac{1}{5}(0) - \frac{2}{3} = 0 - \frac{2}{3} = -\frac{2}{3}
   \]
   So, \( y = -\frac{2}{3} \).

3. **For \( x = 1 \):**
   \[
   y = \frac{1}{5}(1) - \frac{2}{3} = \frac{1}{5} - \frac{2}{3} = \frac{3}{15} - \frac{10}{15} = -\frac{7}{15}
   \]
   So, \( y = -\frac{7}{15} \).

4. **For \( x = 2 \):**
   \[
   y = \frac{1}{5}(2) - \frac{2}{3} = \frac{2}{5} - \frac{2}{3} = \frac{6}{15} - \frac{10}{15} = -\frac{4}{15}
   \]
   So, \( y = -\frac{4}{15} \).

### Now, let's compare the results to the options:

- **Option A**: \((-1, -\frac{13}{15}), (0, -\frac{2}{3}), (1, -\frac{7}{15}), (2, -\frac{4}{15})\)
- **Option B**: \((-1, \frac{13}{15}), (0, -\frac{2}{3}), (1, -\frac{7}{15}), (2, -\frac{4}{15})\)
- **Option C**: \((-1, -\frac{13}{15}), (0, -\frac{2}{3}), (1, -\frac{7}{15}), (2, -\frac{4}{15})\)
- **Option D**: \((-1, -1\frac{1}{2}), (0, -\frac{2}{3}), (1, -\frac{1}{2}), (2, 0)\)

Both **Options A** and **Option C** have the correct \( y \)-values for all points. Since they are identical, either one is correct.

The correct answer is **Option A** (or equivalently, Option C).

Would you like further details on this or have any other questions? 

Here are some related questions:
1. How can you derive the slope-intercept form of a linear equation?
2. How do you handle fractions when solving for function values?
3. Can a function graph ever have two different \( y \)-values for the same \( x \)-coordinate?
4. What is the significance of the slope in the equation \( y = \frac{1}{5}x - \frac{2}{3} \)?
5. What methods can be used to graph linear functions?

**Tip:** Always simplify fractions early when solving for \( y \) in linear equations to make calculations easier.

Which set of ordered pairs is made up of points on the graph of the function y = (1/5)x - (2/3)?

Learn how to verify if a set of ordered pairs corresponds to points on the graph of the linear function y = (1/5)x - (2/3). This exercise covers key algebraic concepts such as graphing linear equations and slope-intercept form. Suitable for students in Grades 8-10.

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