To find the point-slope form of the equation for the line passing through the points $(2, -1)$ and $(3, 5)$, we'll follow these steps:

1. Find the slope ($m$): $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-1)}{3 - 2} = \frac{6}{1} = 6$

2. Use the point-slope form equation: $y - y_1 = m(x - x_1)$ Substitute one of the points (either $(2, -1)$ or $(3, 5)$) and the slope $m = 6$ into the equation.

   Using the point $(2, -1)$: $y - (-1) = 6(x - 2)$ Simplifying this: $y + 1 = 6(x - 2)$

This matches the first option in your provided choices:

• $\boxed{y + 1 = 6(x - 2)}$

Would you like more details on any part of this solution, or do you have any other questions?

Here are five related questions:

1. How do you convert from point-slope form to slope-intercept form?
2. What is the equation of the line in standard form that passes through the points $(2, -1)$ and $(3, 5)$?
3. How would the equation change if the line had a negative slope?
4. How do you find the equation of a line given only the slope and y-intercept?
5. What would be the equation if the points were swapped, i.e., $(3, 5)$ to $(2, -1)$?

Tip: The point-slope form is particularly useful for finding the equation of a line quickly when you know one point on the line and the slope.