Find the slope of the line through the points \( (1,4) \) and \( (7,1) \). A \( -\frac{1}{2} \) B -2 (C) \( \frac{1}{2} \) (D) 2

To find the slope of the line through the points \( (1, 4) \) and \( (7, 1) \), we can use the formula for the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (7, 1) \). Plugging in these values: \[ m = \frac{1 - 4}{7 - 1} = \frac{-3}{6} = -\frac{1}{2} \] So the slope of the line is \( -\frac{1}{2} \), which corresponds to option A! Now, did you know that slope is a crucial concept in understanding linear relationships in math and science? It essentially tells us how steep a line is on a graph, whether it's tilting upwards or downwards, and helps us understand how variables interact. If you're ever unsure whether your slope calculation is correct, a good tip is to always remember that for every increase in the x-direction, the result in y-direction can either go up (positive slope) or go down (negative slope). Common mistakes include mixing up the order of the points, so always keep \( y_2 \) and \( y_1 \) straight!