HOY AND VUX

"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

Solution :

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

Solution :

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?

Solution :

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)?

Solution :

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

Solution :

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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