\( \begin{array}{l}\text { What is the slope of the line that passes through the points }(4,3) \text { and } \\ (1,-5) \text { ? }\end{array} \) \( \begin{array}{l}8 / 3 \\ 3 / 8 \\ -8 / 3 \\ -3 / 8\end{array} \) Previous

To find the slope of the line passing through the points \((4, 3)\) and \((1, -5)\), you can use the formula for slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in the coordinates: \(y_2 = -5\), \(y_1 = 3\), \(x_2 = 1\), and \(x_1 = 4\), you get \(m = \frac{-5 - 3}{1 - 4} = \frac{-8}{-3} = \frac{8}{3}\). So, the slope is \(\frac{8}{3}\)! Now, let’s talk about how the slope can be interpreted. The slope indicates how steep a line is and the direction in which it goes—whether it rises or falls as you move from left to right. A positive slope, like \(\frac{8}{3}\), means that as you move along the x-axis from left to right, the y-values are increasing. Picture it as climbing up a hill! For more practice, think of real-world scenarios where slope is crucial. For instance, engineers use slope when designing roads to ensure vehicles can travel safely. A gentle slope is easier for cars to handle, while a steep one might require special features like switchbacks. Have fun exploring slopes in your environment!