Understanding Negative Slope in Mathematics: An Explanation and Graphical Illustration

negative slope

Negative slope refers to the downward or descending direction of a line on a graph

Negative slope refers to the downward or descending direction of a line on a graph. In mathematics, slope measures the steepness of a line and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

A negative slope means that as the value of the independent variable (usually represented on the x-axis) increases, the value of the dependent variable (usually represented on the y-axis) decreases. In other words, for every unit increase in the x-coordinate, there is a corresponding decrease in the y-coordinate.

Graphically, a line with a negative slope will slant downwards from left to right. The steeper the slope, the more rapid the decrease in the y-values as the x-values increase.

To illustrate, consider the equation of a straight line in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept (the point at which the line intersects the y-axis).

If the slope (m) is negative, then the line will have a negative slope. For example, if the equation of the line is y = -2x + 5, the negative coefficient (-2) indicates a negative slope. This means that for each unit increase in x, the corresponding y-value decreases by 2 units.

You can also identify a negative slope by comparing two points on the line. If the y-coordinate decreases as the x-coordinate increases, the slope is negative.

In summary, a negative slope refers to a line that descends from left to right. It indicates a decreasing relationship between the x and y coordinates, where the y-values decrease as the x-values increase.

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