You have the equation of a line:

$y = \frac{2}{3}x + 2$

and the point $(6, -1)$. To determine if the point $(6, -1)$ lies on the line, substitute $x = 6$ into the equation and check if the resulting $y$-value equals $-1$.

1. Substituting $x = 6$ into the equation:

$y = \frac{2}{3}(6) + 2$

Simplifying:

$y = \frac{12}{3} + 2 = 4 + 2 = 6$

Since the calculated $y$-value is 6 and not $-1$, the point $(6, -1)$ does not lie on the line.

Would you like to see a step-by-step breakdown of the solution or have any other questions?

Here are 5 related questions:

1. How can we find the distance between the point and the line?
2. How would you determine the slope of a line perpendicular to this one?
3. How do you find the equation of a line passing through the point $(6, -1)$ and parallel to the given line?
4. How would you graph this line and the point $(6, -1)$?
5. What is the x-intercept of the line $y = \frac{2}{3}x + 2$?

Tip: When checking if a point lies on a line, substitute both the x- and y-values into the equation. If both sides balance, the point is on the line.