Find the slope of the line that passes through \( (2,2) \) and \( (5,3) \). 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 \( (2, 2) \) and \( (5, 3) \), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (2, 2) \) and \( (x_2, y_2) = (5, 3) \). Substituting in the values: \[ m = \frac{3 - 2}{5 - 2} = \frac{1}{3} \] So, the slope of the line is \( \frac{1}{3} \). --- Not only does the slope of the line give you a sense of how steep the line is, but it also tells you the direction the line is going. A positive slope means the line rises as you move from left to right (like climbing a hill), while a negative slope means it falls (like descending). If you're looking to visualize this, simply sketch the two points on a graph and draw a line connecting them. You’ll see that for every 3 units you move horizontally to the right, the line moves up 1 unit. This can help solidify concepts about slope for future math adventures!