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To determine which of the given points lies on the line described by the equation \( y - 3 = 5(x - 9) \), we can substitute the coordinates of each point into the equation and check if both sides are equal.

### Step 1: Simplify the equation
The given equation is:

\[
y - 3 = 5(x - 9)
\]

Distribute the 5 on the right-hand side:

\[
y - 3 = 5x - 45
\]

Now, solve for \( y \):

\[
y = 5x - 42
\]

### Step 2: Check each point

We will substitute each point's \(x\) and \(y\) values into the equation \( y = 5x - 42 \) and verify which one satisfies it.

#### Option A: (3, 9)
Substitute \( x = 3 \) and \( y = 9 \) into the equation:

\[
9 = 5(3) - 42
\]
\[
9 = 15 - 42
\]
\[
9 \neq -27 \quad (\text{False})
\]

#### Option B: (-3, -9)
Substitute \( x = -3 \) and \( y = -9 \) into the equation:

\[
-9 = 5(-3) - 42
\]
\[
-9 = -15 - 42
\]
\[
-9 \neq -57 \quad (\text{False})
\]

#### Option C: (-9, -3)
Substitute \( x = -9 \) and \( y = -3 \) into the equation:

\[
-3 = 5(-9) - 42
\]
\[
-3 = -45 - 42
\]
\[
-3 \neq -87 \quad (\text{False})
\]

#### Option D: (9, 3)
Substitute \( x = 9 \) and \( y = 3 \) into the equation:

\[
3 = 5(9) - 42
\]
\[
3 = 45 - 42
\]
\[
3 = 3 \quad (\text{True})
\]

### Conclusion:
The point \( (9, 3) \) lies on the line. Therefore, the correct answer is **Option D: (9, 3)**.

Would you like any further details or explanations?

Here are 5 related questions for practice:
1. How do you convert an equation from point-slope form to slope-intercept form?
2. What is the slope of the line given by the equation \( y - 3 = 5(x - 9) \)?
3. How do you determine if a point lies on a given line algebraically?
4. What is the equation of a line passing through the points (1, 2) and (3, 4)?
5. How do you find the y-intercept of a line in point-slope form?

**Tip:** When checking if a point lies on a line, always substitute both the x and y coordinates into the equation to verify the equality.

Which of these points lies on the line described by the equation below?

y - 3 = 5(x - 9)

A. (3, 9)
B. (-3, -9)
C. (-9, -3)
D. (9, 3)

Determine which point lies on the line described by the equation y - 3 = 5(x - 9). Learn how to substitute coordinates and simplify equations. Suitable for students in Grades 7-9.

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