Determine the slope of the line passing through the given points. \[ (-5,-4) \text { and }(-1,3) \] The slope of the line is

To find the slope of the line passing through the points \((-5,-4)\) and \((-1,3)\), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (-5, -4)\) and \((x_2, y_2) = (-1, 3)\). Substituting the values: \[ m = \frac{3 - (-4)}{-1 - (-5)} = \frac{3 + 4}{-1 + 5} = \frac{7}{4} \] So, the slope of the line is \(\frac{7}{4}\). The slope of the line represents the steepness and direction of the line on a graph. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. In this case, a slope of \(\frac{7}{4}\) suggests that for every 4 units you move horizontally to the right, the line rises 7 units vertically. When calculating the slope, a common mistake is to miscount signs. Always ensure you’re subtracting the correct \(y\) values and the correct \(x\) values. Double-checking your work can save you from ending up with the wrong answer!