explain why the slope of a horizontal line is always zero
since the line is horizontal, the y-value is always the same.
So, the slope,
∆y/∆x = 0/∆x
which is always zero.
slope is rise/run, so if the rise is zero, so is the slope.
If a line is horizontal, then all its points are the same distance away, either above or below, from the x-axis, that is,
any two points would have the form (x1,y) and (x2,y)
slope = (y-y)/(x2 - x1) = 0/(x2 - x1) = 0 , assuming x1 ≠ x2
The slope of a line represents the steepness or slanting of the line. It can be understood as the measure of how much the line rises or falls for each unit change in the x-axis.
In the case of a horizontal line, it means that the line has no slant or rise. It is perfectly flat and parallel to the x-axis.
To calculate the slope of a line, we use the formula: slope = (change in y)/(change in x).
For a horizontal line, there is no change in y because the line does not rise or fall. However, there may be a change in x, as the line extends along the x-axis.
Since there is no change in y and a non-zero change in x, the slope, as calculated, will be zero divided by a non-zero value. Any number divided by a non-zero value is always zero.
Therefore, the slope of a horizontal line is always zero.
The slope of a line represents the rate at which the line is inclined or tilted. In the case of a horizontal line, it is perfectly flat and does not tilt or incline in any direction. Therefore, the slope of a horizontal line is always zero.
To understand why the slope of a horizontal line is zero, we need to recall the formula for calculating slope:
Slope (m) = (change in y-coordinates) / (change in x-coordinates).
For a horizontal line, the change in the y-coordinates are always zero, as the line does not move vertically. Since any number divided by zero is undefined, the slope of a horizontal line cannot be calculated using the formula. However, we can observe that the change in x-coordinates is not zero, regardless of the distance between two points on the line.
Hence, when we substitute the values into the slope formula, we get:
Slope (m) = 0 / (change in x-coordinates) = 0.
This demonstrates that the slope of a horizontal line is always zero.