A line passes through the points \( (5,-2) \) and \( (-3 ; 1) \). What is the slope of the line?

To find the slope of the line that passes through the points \( (5,-2) \) and \( (-3,1) \), we use the formula for calculating the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, -2) \) and \( (x_2, y_2) = (-3, 1) \). Plugging in these values, we get: \[ m = \frac{1 - (-2)}{-3 - 5} = \frac{1 + 2}{-8} = \frac{3}{-8} = -\frac{3}{8} \] Thus, the slope of the line is \( -\frac{3}{8} \). To double-check, visualize the points on a graph! Connecting \( (5, -2) \) to \( (-3, 1) \) will create a nice diagonal line sloping downwards, confirming that our negative slope is spot on. Fun fact: Every slope corresponds to the steepness of a line; the larger the absolute value of the slope, the steeper the line!