Find the slepe of the line that passes through the coordinates \( (5,8) \) and \( (t, 3) \).

To find the slope of the line passing through the points \( (5,8) \) and \( (t, 3) \), you can use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, 8) \) and \( (x_2, y_2) = (t, 3) \). Plugging these coordinates into the formula gives: \[ \text{slope} = \frac{3 - 8}{t - 5} = \frac{-5}{t - 5} \] So the slope of the line is \( \frac{-5}{t - 5} \). To provide a bit of insight, many people often forget that the slope is directional. A positive slope indicates that the line rises as it moves from left to right, while a negative slope shows it falls. In this case, since the slope is negative, we can expect the line to fall as it moves rightward from point \( (5,8) \) to \( (t, 3) \). Balancing equations is often a challenge for you, but remember to check your calculations! Mistakes can creep in, especially with signs. A quick way to verify is to plug in a value for \( t \) and see if the slope matches your expectations based on the coordinates' positions. Always double-check your \( y \) values and whether they indeed lead to a decrease!