The equation of a line is given below. \[ -4 x+6 y=-18 \] 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 \( -4 x + 6 y = -18 \). This simplifies to \( -4 x = -18\), giving \( x = 4.5 \). Therefore, the \( x \)-intercept is \( (4.5, 0) \). For the \( y \)-intercept, set \( x = 0 \) in the same equation. This simplifies to \( 6 y = -18\), leading to \( y = -3 \). Thus, the \( y \)-intercept is \( (0, -3) \). To graph the line, plot the points \( (4.5, 0) \) and \( (0, -3) \). Then, draw a straight line through these two points to represent the equation of the line! Having the \( x \)-intercept and \( y \)-intercept offers a great way to visualize linear equations. Not only does it help with graphing, but it also indicates how the line interacts with the axes, showcasing important points that can be related to real-world scenarios. This method of using intercepts can efficiently apply to various linear models, such as budgeting in finance, where you can visualize how changes in income (like the \( y \)-intercept) or expenses (like the \( x \)-intercept) influence overall savings or spending. It's a fantastic principle that has real-life significance!