To complete this table, let's evaluate the equation $y = \frac{1}{3}x + 2$ for $x = 0$ and $x = 3$.

1. When $x = 0$: $y = \frac{1}{3}(0) + 2 = 0 + 2 = 2$ So, when $x = 0$, $y = 2$.

2. When $x = 3$: $y = \frac{1}{3}(3) + 2 = 1 + 2 = 3$ So, when $x = 3$, $y = 3$.

Completed Table

Ordered Pairs

The ordered pairs to plot are:

• $(0, 2)$
• $(3, 3)$

Graphing the Linear Equation

To graph, plot these points on the grid:

• Point $(0, 2)$ is on the y-axis at 2.
• Point $(3, 3)$ is to the right of the origin, up at 3.

Connect these points to form a straight line representing the equation $y = \frac{1}{3}x + 2$.

Would you like more details, or have any questions?

Here are five additional questions for exploration:

1. How would the line change if the slope were different?
2. What would the y-intercept be if it shifted up by 1 unit?
3. How do you find the slope from two points on a graph?
4. Can you explain how to graph lines with negative slopes?
5. What if the equation was $y = -\frac{1}{3}x + 2$; how would the graph look?

Tip: When graphing linear equations, always start by plotting the y-intercept, then use the slope to determine the direction and spacing of the line.