The problem asks to find the equation of a line passing through the points $(1, 3)$ and $(7, 2)$.

Steps:

1. Find the slope $m$ using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Where $(x_1, y_1) = (1, 3)$ and $(x_2, y_2) = (7, 2)$.

2. Apply the point-slope form of the line equation: $y - y_1 = m(x - x_1)$ Once we find the slope, substitute $m$, $x_1$, and $y_1$ to get the equation.

Let's calculate the slope and the final equation of the line.

First, calculate the slope $m$: $m = \frac{2 - 3}{7 - 1} = \frac{-1}{6} = -\frac{1}{6}$

Now use the point-slope form: $y - 3 = -\frac{1}{6}(x - 1)$

Simplifying: $y - 3 = -\frac{1}{6}x + \frac{1}{6}$ $y = -\frac{1}{6}x + \frac{1}{6} + 3$ $y = -\frac{1}{6}x + \frac{1}{6} + \frac{18}{6}$ $y = -\frac{1}{6}x + \frac{19}{6}$

Final Equation:

$y = -\frac{1}{6}x + \frac{19}{6}$

Would you like any more details or explanations?

Here are five related questions:

1. How do you derive the slope-intercept form of a line from two points?
2. What is the slope if the two points were $(1, 3)$ and $(7, 5)$?
3. How can you find the equation of a vertical line through two points?
4. How do you interpret the slope of a line geometrically?
5. What is the significance of the $y$-intercept in the equation of a line?

Tip: In any two-point problem, always use the slope formula first to avoid calculation mistakes!