The equation of a line is given below. \[ x-3 y=-6 \] Find the \( x \)-intercept and the \( y \)-intercept. Then use them to graph the line.

To find the \( x \)-intercept, set \( y = 0 \) in the equation: \[ x - 3(0) = -6 \] This simplifies to \( x = -6 \), making the \( x \)-intercept \((-6, 0)\). For the \( y \)-intercept, set \( x = 0 \): \[ 0 - 3y = -6 \] This simplifies to \( -3y = -6 \), giving \( y = 2 \). Thus, the \( y \)-intercept is \( (0, 2) \). Now graph the line by plotting the points \((-6, 0)\) and \( (0, 2)\) and drawing a straight line through them! To add a historical twist, did you know the equation of a line has roots going back to ancient civilizations? The Babylonians and Greeks were already grappling with geometric shapes and their properties, laying a foundation for the algebra we use today! From a practical perspective, understanding intercepts is crucial in fields like economics and engineering. For example, when graphing supply and demand curves, the intercepts indicate where supply meets demand, guiding decisions on pricing strategies and product releases!