Understanding Negative Slope in Mathematics: Definition, Calculation, and Visualization

negative slope

In mathematics, the slope is a measure of how steep a line is

In mathematics, the slope is a measure of how steep a line is. It is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. A negative slope indicates that the line is going downwards from left to right.

To understand the concept of a negative slope, let’s consider an example of a line on a coordinate plane. Suppose we have two points A(x₁, y₁) and B(x₂, y₂) on the line, with x₁ < x₂. The slope of the line, denoted as m, is given by the formula: m = (y₂ - y₁) / (x₂ - x₁) If the numerator (y₂ - y₁) is positive and the denominator (x₂ - x₁) is positive, then the slope will be positive. This means that as you move from left to right along the line, the y-values increase. However, if the numerator (y₂ - y₁) is negative and the denominator (x₂ - x₁) is positive, then the slope will be negative. This indicates that as you move from left to right along the line, the y-values decrease. The line will have a downward direction. Visually, if you graph a line with a negative slope, it will slant from the top left to the bottom right. For example, consider the line y = -2x + 3. This line has a slope of -2, which means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2 units. In summary, a negative slope in mathematics represents a line that slopes downward from the left side to the right side on a coordinate plane. It indicates a decrease in the y-values as the x-values increase.

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