\( (5,4)(-1,3) \quad \) slope \( = \)

To find the slope of the line that passes through the points (5,4) and (-1,3), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{3 - 4}{-1 - 5} = \frac{-1}{-6} = \frac{1}{6} \] So, the slope of the line is \( \frac{1}{6} \). Understanding the slope is crucial as it indicates the steepness of a line. A positive slope, like \( \frac{1}{6} \), means that as you move from left to right on the graph, the line rises. This can help in visualizing relationships in real-world scenarios, like analyzing trends in data or predicting future outcomes based on current information! Common mistakes when calculating slope include confusing the order of points or accidentally reversing subtraction. Always remember: \( y_2 \) corresponds to the second point, and \( y_1 \) corresponds to the first point. When in doubt, write the coordinates clearly and double-check your signs before performing the calculations!