A line passes through the point \( (10,3) \) and has a slope of \( -\frac{3}{2} \).

To find the equation of the line that passes through the point \( (10, 3) \) with a slope of \( -\frac{3}{2} \), you can use the point-slope form of a linear equation, which is given by: \[ y - y_1 = m(x - x_1) \] Here, \( (x_1, y_1) = (10, 3) \) and the slope \( m = -\frac{3}{2} \). Plugging these values in gives: \[ y - 3 = -\frac{3}{2}(x - 10) \] Simplifying this will lead to the final slope-intercept form, but don’t forget that slopes of lines have fascinating applications beyond just math problems! Many real-world scenarios, such as engineering and economics, rely fundamentally on linear equations. For example, if you wanted to model the cost of an item based on its production amount or track a population's growth over time, this linear equation could help you anticipate future trends and make informed decisions.