The topic of horizontal lines comes from the branch of mathematics called coordinate geometry. These are straight lines that are drawn from left to right or vice versa. These horizontal lines are parallel to the x-axis in the coordinate plane.
The line which only has intercepts on the y-axis but not on the x-axis is called a horizontal line. The horizontal lines are also called sleeping lines.
The slope of a horizontal will always be zero. Therefore, when we try to calculate the slope of a horizontal line, there is no change in y – coordinates as it is the same throughout the horizontal line.
Let us see an example of how the slope of a horizontal line is eventually 0.
From the above figure, keep a point randomly on the coordinate plane, let's say (-3, 3). Hence, you know that the y – coordinate of the given point is y = 3.
Now, try to plot some more points where the y – coordinate is the same as before. Let's say (0, 3), (2, 3), (5, 3).
Observe carefully that there is no change in the y – coordinates, and it remains as a straight horizontal line.
Now join all the points from left to right to get a horizontal line. Hence, the slope of a horizontal line is 0.
d that there is no x present, i.e., the x-intercept can be any point, but the y – coordinate of all the plotted points must be the same, i.e., y = b.
The y-intercept of a horizontal line is (0, b).
From the above-plotted points, (a, b) : (-3, 3), (0, 3), (2, 3), (5, 3), all the y – coordinates are constant, which is 3. Hence, the horizontal line equation is y = 3.
The horizontal line test is mainly used to determine whether the given function is a one – to – one function.
According to the horizontal line test, a horizontal line passing through more than one point is not a one–to–one function.
From the above fig., we can observe that the line is only passing through one point on the graph, so that it is a one–to–one.
And now, from the above fig., we get to know that it is NOT a one–to–one function as the line is passing through more points.
Finally, the horizontal line test is the easiest and effective way of checking whether the function is one–to–one or not.