To determine whether the point \( P = (2, -3) \) lies on the line \( y = -3x + 1 \), we can substitute the \( x \) and \( y \) coordinates of the point into the equation of the line and check if the equation holds true.

Given:
- The equation of the line: \( y = -3x + 1 \)
- The point \( P = (2, -3) \)

Substitute \( x = 2 \) and \( y = -3 \) into the equation:

\[
y = -3(2) + 1
\]

Calculate the right-hand side:

\[
y = -6 + 1 = -5
\]

Since the left-hand side is \( -3 \) (from the point \( P \)), and the right-hand side is \( -5 \), the point \( P = (2, -3) \) **does not** lie on the line \( y = -3x + 1 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the significance of the slope in the equation of a line?
3. How can you find the y-intercept from the equation of a line?
4. How do you determine if two lines are parallel or perpendicular?
5. What is the general form of a linear equation?

**Tip:** Always double-check your substitution when verifying if a point lies on a line, to ensure accuracy.

Check if the point (2, -3) lies on the line y = -3x + 1 using a simple substitution method. This detailed solution guides students through verifying points on a line with clear steps and explanations. Suitable for Grades 6-8.

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