Simplify the equation if possible. Find the x-intercept and the \( y \)-intercept. Then graph the equation. \( -2 x-9 y=9 \)

To simplify the equation, we can rewrite it in slope-intercept form \( y = mx + b \). Starting with \( -2x - 9y = 9 \), we can isolate \( y \): \[ -9y = 2x + 9 \] \[ y = -\frac{2}{9}x - 1 \] Now, for the x-intercept, we set \( y = 0 \): \[ 0 = -\frac{2}{9}x - 1 \implies \frac{2}{9}x = -1 \implies x = -\frac{9}{2} = -4.5 \] For the y-intercept, we set \( x = 0 \): \[ y = -\frac{2}{9}(0) - 1 = -1 \] So, the x-intercept is \((-4.5, 0)\) and the y-intercept is \((0, -1)\). To graph the equation, plot these intercepts and draw a straight line through them. For some fun facts, did you know that intercepts can help you quickly sketch a graph without needing to plot multiple points? Just grab those intercepts and connect the dots! Also, keep in mind that slopes like the one from this equation represent the steepness of the line – here, it’s negative! So you're looking at a descending line that goes down from left to right, adding flair to your graphing skills!