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The question asks to find the equation of the line that passes through two given points: \( (6, 0) \) and \( (0, 2) \).

### Step 1: Calculate the slope of the line
The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For the points \( (6, 0) \) and \( (0, 2) \):
- \( x_1 = 6 \), \( y_1 = 0 \)
- \( x_2 = 0 \), \( y_2 = 2 \)

\[
m = \frac{2 - 0}{0 - 6} = \frac{2}{-6} = -\frac{1}{3}
\]

### Step 2: Use the point-slope form of the equation of a line
The point-slope form is given by:

\[
y - y_1 = m(x - x_1)
\]

Substitute \( m = -\frac{1}{3} \) and use the point \( (6, 0) \):

\[
y - 0 = -\frac{1}{3}(x - 6)
\]

Simplify:

\[
y = -\frac{1}{3}x + 2
\]

### Final Answer:
The equation of the line is:

\[
y = -\frac{1}{3}x + 2
\]

Would you like any further clarification or details?

### Follow-up Questions:
1. How is the slope of a line interpreted geometrically?
2. What happens if both points have the same \( x \)-coordinates?
3. Can you explain how to derive the equation using the point \( (0, 2) \) instead?
4. How does the slope-intercept form differ from the point-slope form?
5. How do vertical and horizontal lines differ in their equations?

### Tip:
When finding the slope, remember that dividing by zero results in an undefined slope, indicating a vertical line!

Write the equation of the line that passes through the points (6, 0) and (0, 2).

Learn how to calculate the equation of a line passing through the points (6, 0) and (0, 2). This problem includes finding the slope and applying the point-slope form to derive the equation in slope-intercept form. Suitable for students in Grades 7-10.

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