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To solve the given problem, we need to find the equation of a line passing through two points, \( (6, 1) \) and \( (3, 3) \).

We can do this by using the **point-slope form** of the equation of a line:

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

where \( m \) is the slope of the line, and \( (x_1, y_1) \) is a point on the line.

### Step 1: Calculate the slope
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Substituting the given points \( (6, 1) \) and \( (3, 3) \):

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

### Step 2: Use the point-slope form
Using one of the points, say \( (3, 3) \), and the slope \( m = -\frac{2}{3} \), we can plug these values into the point-slope equation:

\[
y - 3 = -\frac{2}{3}(x - 3)
\]

### Step 3: Simplify to slope-intercept form
Now, let's simplify the equation:

\[
y - 3 = -\frac{2}{3}(x - 3)
\]

Distribute the slope:

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

Add 3 to both sides:

\[
y = -\frac{2}{3}x + 5
\]

Thus, the equation of the line is:

\[
y = -\frac{2}{3}x + 5
\]

You can now submit this equation as the answer.

Would you like further explanation or details? Here are some additional questions to expand your understanding:

1. How do you convert a line equation from point-slope form to slope-intercept form?
2. What is the significance of the slope being negative in this problem?
3. How would the equation change if the points were flipped, i.e., \( (3, 3) \) and \( (6, 1) \)?
4. Can you determine the x- and y-intercepts from the equation?
5. How do parallel and perpendicular lines relate to this equation?

**Tip:** Always double-check the sign of the slope when calculating between two points.

What is an equation of the line that passes through the points (6, 1) and (3, 3)?

Learn how to find the equation of a line passing through the points (6, 1) and (3, 3). This problem covers algebraic concepts like slope calculation and point-slope form, suitable for students in Grades 8-10.

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