Complete the table and then graph the function.
y=
1

5
x
x	y
0
5
10
Click to select points on the graph.

To complete the table and graph the function \( y = \frac{1}{5}x \), we'll first calculate the value of \( y \) for each given value of \( x \).

### Step 1: Calculate the \( y \)-values

Given the function \( y = \frac{1}{5}x \):

- When \( x = 0 \): 
  \[
  y = \frac{1}{5} \times 0 = 0
  \]
- When \( x = 5 \): 
  \[
  y = \frac{1}{5} \times 5 = 1
  \]
- When \( x = 10 \): 
  \[
  y = \frac{1}{5} \times 10 = 2
  \]

### Completed Table

\[
\begin{array}{c|c}
x & y \\
\hline
0 & 0 \\
5 & 1 \\
10 & 2 \\
\end{array}
\]

### Step 2: Graph the Function

The points to plot on the graph are:
- \( (0, 0) \)
- \( (5, 1) \)
- \( (10, 2) \)

These points should form a straight line since the equation is linear. The line will have a slope of \( \frac{1}{5} \).

Would you like a detailed explanation of the graphing process, or do you have any other questions?

### Related Questions:
1. What is the slope of the function \( y = \frac{1}{5}x \) and how is it interpreted?
2. How would the graph change if the function were \( y = \frac{2}{5}x \) instead?
3. How do you find the \( y \)-intercept of a linear function?
4. What happens to the graph if you shift it up by 2 units?
5. How would you graph the function \( y = -\frac{1}{5}x \)?

**Tip:** When graphing linear functions, always start by identifying key points like the \( y \)-intercept and another point on the line to ensure accuracy.

Learn how to complete the table and graph the linear function y = (1/5)x with a step-by-step solution. This problem involves calculating values for x and corresponding y, plotting points on a graph, and understanding the concept of slope. Suitable for Grades 7-9 students learning linear functions and graphing.

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