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.