Find an equation of the line that passes through the origin and has a slope of -2 . The equation of the line is \( \square \). (Simplify your answer. Type your answer in slope-intercept form.)

To find the equation of the line that passes through the origin with a slope of -2, we can use the slope-intercept form of a linear equation, which is given by: \[ y = mx + b \] Here, \( m \) is the slope and \( b \) is the y-intercept. Since the line passes through the origin, the y-intercept \( b \) is 0. Substituting the slope and the y-intercept into the equation gives us: \[ y = -2x + 0 \] Simplifying this, we arrive at the final equation: \[ y = -2x \] So, the equation of the line is \( y = -2x \). Now, let’s dive into the story behind negative slopes and how they interact with graphing. In math, a negative slope means that as you move from left to right on the graph, the line goes downwards, much like a slide at the playground! It indicates an inverse relationship between x and y, meaning if one goes up, the other comes down. Also, when you create a graph with this equation, it’s a fantastic visual of how linear equations work. You can even plot additional points! If you input x-values like 1, 2, or -1, -2, you’ll see how the points align and illustrate the relationship defined by the equation. It’s a great way to get comfortable with graphing slopes and intercepts!