To write the equation of a line in point-slope form, we first need to calculate the slope ($m$) using the two points provided: $(2, 3)$ and $(3, 7)$.

Step 1: Calculate the slope ($m$)

The slope formula 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: $m = \frac{7 - 3}{3 - 2} = \frac{4}{1} = 4$

Step 2: Use the point-slope formula

The point-slope form of a line is: $y - y_1 = m(x - x_1)$

We can use either of the given points. Let's use $(2, 3)$: $y - 3 = 4(x - 2)$

This is the equation of the line in point-slope form.

Would you like further details on solving this, or any additional clarifications?

Here are some related questions to expand your understanding:

1. How do you convert the point-slope form to slope-intercept form?
2. What would the equation look like if you used the point $(3, 7)$ instead?
3. Can you use the point-slope form to find the equation of a line perpendicular to this one?
4. How would you determine if a third point lies on this line?
5. What is the significance of the slope value in this line's equation?

Tip: When working with two points, always ensure you compute the slope first, as this defines the steepness and direction of the line.