The problem asks to identify which ordered pair lies on the same line as the points shown in the graph.

Step-by-step solution:

1. Determine the equation of the line: Observing the graph, we see that the line passes through these points:

   • $(-6, -4)$
   • $(0, 0)$ (the origin)

   Using these points, calculate the slope $m$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-4)}{0 - (-6)} = \frac{4}{6} = \frac{2}{3}.$

   Since the line passes through the origin, its equation is: $y = \frac{2}{3}x.$

2. Check which ordered pair satisfies $y = \frac{2}{3}x$: Evaluate each option:

   • $(2, 3)$: $y = \frac{2}{3}(2) = \frac{4}{3} \neq 3$, not on the line.
   • $(3, 2)$: $y = \frac{2}{3}(3) = 2$, on the line.
   • $(4, 6)$: $y = \frac{2}{3}(4) = \frac{8}{3} \neq 6$, not on the line.
   • $(6, 4)$: $y = \frac{2}{3}(6) = 4$, on the line.

3. Correct options: Both $(3, 2)$ and $(6, 4)$ lie on the line.

If you have additional questions, need further explanation, or want detailed steps for something else, let me know!

Related Questions to Deepen Understanding:

1. How do you calculate the slope of a line given two points?
2. What is the general equation of a line in slope-intercept form?
3. How do you test if a point lies on a given line?
4. How can you derive the equation of a line that does not pass through the origin?
5. What happens if the slope of a line is zero or undefined?

Tip:

Always write the equation of the line before checking points—it simplifies the process and ensures accuracy!