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.

Find out if the point (6, -1) lies on the line y = 2/3x + 2 with a clear step-by-step solution. This problem covers key concepts in linear equations and coordinate geometry, suitable for students in Grades 8-10.

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