Find the \( y \)-intercept of the line \( y=-\frac{15}{8} x+9 \). Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

To find the \( y \)-intercept of the line given by the equation \( y=-\frac{15}{8} x+9 \), you need to determine the value of \( y \) when \( x = 0 \). Plugging \( x = 0 \) into the equation gives: \[ y = -\frac{15}{8}(0) + 9 = 0 + 9 = 9. \] Thus, the \( y \)-intercept is \( 9 \). For a line, the \( y \)-intercept is where it crosses the \( y \)-axis, and this visual understanding can really help in graphing. Imagine plotting this line on a graph; it intercepts the vertical axis at the point \( (0, 9) \), making it clear that the height of 9 is where you'll find this line slicing through the \( y \)-axis. Additionally, knowing \( y \)-intercepts is crucial in real-world applications; for instance, in business, the \( y \)-intercept can represent initial costs or revenue when no products are sold, helping in budget forecasts and financial planning.