The problem asks to find the equation of a line in slope-intercept form, given two points: $(5, 1)$ and $(2, -2)$.

Steps:

1. Calculate the slope (m) using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points: $m = \frac{-2 - 1}{2 - 5} = \frac{-3}{-3} = 1$

2. Use the point-slope formula to find the equation of the line. The point-slope formula is: $y - y_1 = m(x - x_1)$ Using the point $(5, 1)$ and slope $m = 1$: $y - 1 = 1(x - 5)$ Simplifying: $y - 1 = x - 5$ Add 1 to both sides: $y = x - 4$

Final answer:

The equation of the line in slope-intercept form is: $y = x - 4$

Would you like more details on any part of the solution or have any other questions?

Here are 5 related questions to consider:

1. How would the equation change if one of the points was different?
2. What is the geometric meaning of the slope?
3. How can we find the x- and y-intercepts from this equation?
4. What happens if the slope were negative?
5. How can the distance between the two points be calculated?

Tip: The slope of a line describes how steep the line is. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.