"HOY and VUX" are two words that can be very helpful when dealing with slopes of vertical and horizontal lines.
What is horizontal line ?
The line which is parallel to x- axis is known as horizontal line.
What is vertical line ?
The line which is perpendicular to x-axis is known as vertical line.
What is slope ?
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Let us see some examples based on the above concept.
Example 1 :
Find the slope of the line y = -3
Since the given line is in the form of y = a constant, it remembers the word (HOY). From this we come to know the given line is horizontal line.
Hence its slope is zero.
Example 2 :
Find the slope of the line x = 5
Since the given line is in the form of x = a constant, it remembers the word (VUX). From this we come to know that the given line is vertical line.
Hence its slope is undefined.
Example 3 :
What is the equation of a line that passes through the point (3,-5) and has an undefined slope?
Since the slope of the line passes which through the point (3, -5) is undefined, it should be vertical line.
This remembers the word "VUX". So the equation is in the form x = a constant.
Hence equation of the required line is x = 3.
Example 4 :
What is the equation of the line that has slope=0 and passes through (-2,-5)?
Since the slope of the required line is 0. It must be a horizontal line. So will be in the form of y = a constant.
Hence the equation of the required line is y = -5
Example 5 :
What is the slope of the line parallel to y = -8
y = -8 is a vertical line. The line which is parallel to y = -8 is also a vertical line.
Hence its slope = undefined
After having gone through the stuff given above, we hope that the students would have understood "HOY and VUX".
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