Find the \( y \)-intercept: \( y=-\frac{2}{3} x-4 \)

To find the \( y \)-intercept of the equation \( y = -\frac{2}{3} x - 4 \), set \( x = 0 \). Substituting \( 0 \) for \( x \) gives \( y = -\frac{2}{3}(0) - 4 = -4 \). So, the \( y \)-intercept is \( (0, -4) \). The \( y \)-intercept is where the line crosses the \( y \)-axis, and it’s a fantastic way to understand where your graph starts. Each linear equation can be dissected this way, allowing for easy plotting on a Cartesian plane. Just remember, for any equation in the form of \( y = mx + b \), the \( b \) value directly represents the \( y \)-intercept. For better visualization, grab a piece of graph paper or use an online graphing tool! Plot the \( y \)-intercept first at \( (0, -4) \) and then use the slope, which is \( -\frac{2}{3} \), to find another point. From \( (0, -4) \), you can go down 2 units and right 3 units to plot another point, which will help you draw the line accurately! This technique makes graphing much easier and lets you visualize the linear relationship in the equation.