zero slope
In mathematics, the slope refers to the steepness or inclination of a line
In mathematics, the slope refers to the steepness or inclination of a line. It is a measure of how much a line rises or falls as you move from one point to another along it. A line with a slope of zero means that it doesn’t rise or fall as you move along it, resulting in a horizontal line.
To understand why a line has a zero slope, let’s first define the slope of a line. The slope is calculated by taking the ratio of the change in the vertical coordinates (y-coordinates) to the corresponding change in the horizontal coordinates (x-coordinates) between any two points on the line. Mathematically, the slope (m) is given by:
m = (y2 – y1) / (x2 – x1)
If the numerator, which represents the change in the y-coordinates, is zero, then the slope will be zero regardless of the value of the denominator. This happens when both points on the line have the same y-coordinate. In other words, a line with zero slope is parallel to the x-axis.
For example, let’s consider the line y = 3. This equation represents a horizontal line since the value of y remains constant regardless of the value of x. Choose any two points on this line, say (1, 3) and (5, 3). Applying the slope formula:
m = (3 – 3) / (5 – 1) = 0 / 4 = 0
As you can see, the numerator is zero, resulting in a slope of zero. This indicates that the line is horizontal and doesn’t rise or fall.
In summary, when a line has a zero slope, it means that the line is horizontal and parallel to the x-axis. It doesn’t rise or fall as you move along it.
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