Find the slope of the line that passes through \( (5,1) \) and \( (8,2) \). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

To find the slope of the line that passes through the points \( (5,1) \) and \( (8,2) \), we can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, 1) \) and \( (x_2, y_2) = (8, 2) \). Substituting these values into the formula, we get: \[ m = \frac{2 - 1}{8 - 5} = \frac{1}{3} \] So, the slope of the line is \( \frac{1}{3} \). Choosing two methods to calculate the slope can be a great way to understand the concept! For example, you can visually plot the points on a grid and count the rise (change in y) over run (change in x) or remember that slope represents the steepness of the line, which can also apply in various fields like architecture or even when you're learning to skateboard! For those wanting to delve deeper, consider exploring "The Geometry of Lines" in math textbooks or online resources dedicated to analytic geometry. There are plenty of interactive websites with simulations, equations, and even games that can turn slope calculations into fun visual challenges!