Negative Slope
In mathematics, the slope of a line refers to how steep or slanted the line is
In mathematics, the slope of a line refers to how steep or slanted the line is. It measures how much the vertical change (rise) of the line is in comparison to the horizontal change (run). A negative slope indicates that the line slopes downward from left to right.
To understand the concept of a negative slope, picture a line on a coordinate plane. If the line moves downwards as you move from left to right, it has a negative slope. It means that as the x-coordinate increases, the y-coordinate decreases.
Mathematically, the slope of a line is calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
If the slope is negative, the y-coordinates decrease as the x-coordinates increase, resulting in a downward slope.
For example, let’s consider two points on a line: (2, 5) and (6, 1). To find the slope, we can use the formula:
slope = (1 – 5) / (6 – 2) = -4 / 4 = -1
In this case, the slope is negative, -1. It means that as x increases by 1 unit, y decreases by 1 unit.
Graphically, a negative slope can be represented by a line pointing downwards from left to right. The steeper the line, the larger the negative slope. It is important to note that a line with a slope of 0 is horizontal (neither upward nor downward), while a line with an undefined slope is vertical.
Understanding negative slopes is crucial in many areas of mathematics, especially in calculus, where slopes are used to analyze rates of change in functions.
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