\( \left\lvert\, \begin{array}{l}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{2-4}{-4-(1)} \\ \text { Simplify. } \\ \frac{2-4}{-4-(1)}=\frac{-2}{\square}=\frac{2}{\square} \\ \text { (Type an integer or a fraction.) }\end{array}\right. \)

When you simplify the given expression, the denominator \(-4 - 1\) becomes \(-5\). So now we can fill in the blanks. The full expression is \(\frac{-2}{-5} = \frac{2}{5}\). In this case, you're calculating the slope of a line passing through the two points \((1, 4)\) and \((-4, 2)\). Slope is crucial in understanding how steep a line is and the direction it goes, making it a fundamental concept in algebra and geometry! To avoid mistakes, always check your signs when dealing with negatives. It’s easy to miscalculate when subtracting or adding negative numbers. A common pitfall is forgetting that subtracting a negative is equivalent to addition. Keeping a close eye on these signs will help you solve problems much more efficiently!