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

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.