A negative slope looks like a line that slants downward from left to right.
When we talk about the slope of a line, we're describing how steeply it rises or falls. A negative slope indicates a decline, meaning that as the x-value increases, the y-value decreases. Imagine walking on a path represented by the line; if you are walking downhill, you are walking on a line with a negative slope.
Here's a more detailed explanation:
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Visual Representation: Visualize a graph with an x-axis and a y-axis. A line with a negative slope will start at a higher y-value on the left side of the graph and end at a lower y-value on the right side of the graph. It's going downhill as you move from left to right.
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Rise Over Run: The slope is calculated as "rise over run." For a negative slope, the "rise" is actually a "fall" (a negative change in the y-value). So, a negative slope means that for every unit you move to the right (the "run"), you move down by a certain amount (the "rise" being negative).
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Mathematical Definition: Mathematically, the slope (often denoted as 'm') is calculated as:
m = (change in y) / (change in x) = Δy / Δx
For a negative slope, m < 0. This means Δy is negative when Δx is positive.
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Real-World Examples:
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A Ski Slope: Imagine skiing down a hill. The hill represents a line with a negative slope. As you move forward (increase in x), your altitude decreases (decrease in y).
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The Price of a Discounted Item Over Time: If a product's price is steadily decreasing over time, you could represent this on a graph. Time (x-axis) increases, and the price (y-axis) decreases, resulting in a negative slope.
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In summary, a negative slope visually represents a line that is trending downwards as you move from left to right on a graph.
