To determine if the point $(2, 3)$ lies on the line $3y = -2x + 9$, substitute $x = 2$ and $y = 3$ into the equation and verify if the equation holds true:

Step 1: Substitute $(x, y) = (2, 3)$ into $3y = -2x + 9$

$3(3) = -2(2) + 9$

Step 2: Simplify both sides

$9 = -4 + 9$

Step 3: Evaluate

$9 = 5$

This is not true, so the point $(2, 3)$ does not lie on the line $3y = -2x + 9$.

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Five Related Questions:

1. How do we rewrite the equation of a line in slope-intercept form?
2. What is the slope of the line $3y = -2x + 9$?
3. How can we determine if a point lies on a line geometrically?
4. Can you explain how to find the y-intercept of this line algebraically?
5. How would you check if another point, such as $(0, 3)$, lies on the line?

Tip:

To verify if a point lies on a line, always substitute its coordinates into the equation and check if both sides match.