The equation of a line is given below. \[ 2 x+4 y=-8 \] 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 \( 2x + 4y = -8 \): \[ 2x + 4(0) = -8 \implies 2x = -8 \implies x = -4. \] Thus, the \( x \)-intercept is \((-4, 0)\). Next, to find the \( y \)-intercept, set \( x = 0 \) in the equation: \[ 2(0) + 4y = -8 \implies 4y = -8 \implies y = -2. \] Therefore, the \( y \)-intercept is \((0, -2)\). Now, you can graph the line using these intercepts. Plot the points \((-4, 0)\) and \((0, -2)\) on a coordinate plane, then draw a straight line through these two points. The resulting line represents the equation \( 2x + 4y = -8 \). Now, let's keep this fun! Imagine your graph as a rollercoaster ride, starting at the thrilling heights of the \( y \)-intercept and swooping down to the wild lows of the \( x \)-intercept! Each point represents a unique moment on your graphing adventure. Also, here's a little secret about intercepts: they make great jumping-off points for understanding the behavior of the line. The \( x \)-intercept shows where the ride crosses the ground, while the \( y \)-intercept reveals how low or high the initial ascent takes you. So when you're graphing, remember these points, and they will guide your lines like loyal companions!