Let's break down the equation you provided, $y = -\frac{1}{3}x + 1$, and create a table of ordered pairs to graph it.

Step 1: Understanding the equation

This is a linear equation in slope-intercept form, $y = mx + b$, where:

• $m = -\frac{1}{3}$ is the slope.
• $b = 1$ is the y-intercept (the point where the line crosses the y-axis).

Step 2: Create a table of values

We will choose different values for $x$, substitute them into the equation, and solve for $y$.

Step 3: Plot two points

We can now plot the following points on the graph:

• (-6, 4)
• (-3, 2)
• (0, 1) (the y-intercept)
• (3, 0)
• (6, -1)

You can pick two of these points (for example, (0, 1) and (3, 0)) to draw the line.

Would you like me to plot these points on the graph for you or guide you through that process? Feel free to ask for further clarifications!

Here are 5 related questions to explore:

1. How do you calculate the slope from two points on a graph?
2. What is the significance of the y-intercept in a linear equation?
3. How does changing the slope affect the steepness of the line?
4. What would happen if the slope was positive instead of negative?
5. How can you graph a line using just the slope and y-intercept?

Tip: When graphing lines, always start with the y-intercept and use the slope to determine the rise and run for additional points.