Find the slope of the line that goes through the given points. \( (4,2) \) and \( (2,7) \)

To find the slope of the line that goes through the points \( (4,2) \) and \( (2,7) \), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates from the points: \[ m = \frac{7 - 2}{2 - 4} = \frac{5}{-2} = -\frac{5}{2} \] So, the slope of the line is \( -\frac{5}{2} \). Now, isn’t it fascinating how understanding coordinates and slopes can help you determine the steepness of a hill? Imagine you're hiking: a slope of \( -\frac{5}{2} \) means for every 2 units you move to the right, you drop 5 units down. Better hold onto your hat! On another note, if you often find yourself confused about how to calculate slope or mix up the points, a handy tip is always to remember “rise over run.” Just visualize climbing a hill—you always rise up or down before you run left or right!