To determine which group of ordered pairs lies on the line given by the equation $5x - 2y = 6$, we need to check whether each ordered pair satisfies the equation.

For an ordered pair $(x, y)$ to lie on the line, it must satisfy the equation: $5x - 2y = 6.$ Substitute the $x$ and $y$ values of each pair into this equation and verify if the equation holds.

Please provide the ordered pairs you'd like to test, or I can generate a few to demonstrate.

Would you like to see more details or check a specific group of points?

Here are 5 follow-up questions that might help:

1. What method is used to solve a system of equations with two lines?
2. Can you convert the equation $5x - 2y = 6$ to slope-intercept form?
3. What is the slope of the line $5x - 2y = 6$?
4. What happens if an ordered pair doesn't satisfy the equation of a line?
5. How do you find the x-intercept and y-intercept of the line?

Tip: Converting equations into slope-intercept form $(y = mx + b)$ makes it easier to understand the line's properties.