HOY AND VUX WORKSHEET

Problem 1 :

Find the slope of the line y  =  -3.

Problem 2 :

Find the slope of the line x  =  5.

Problem 3 :

Find which of the following lines are horizontal lines and also write the equations of those lines.

Problem 4 :

Check whether x  =  -2 is a horizontal or vertical line ?

From the above graph, x  =  -2 is a vertical line. 

Problem 5 :

What is the equation of a line that passes through the point (3, -5) and has undefined slope ?

Problem 6 :

What is the equation of the line that has zero slope and passes through the point (-2, -5) ?

Problem 7 :

What is the slope of the line parallel to y  =  -8 ? 

Problem 8 :

What is the slope of the line parallel to x  =  1 ? 

Problem 9 :

What is the slope of the line x  =  0 ? 

Problem 10 :

What is the slope of the line y  =  0 ? 

Solutions

Problem 1 :

Find the slope of the line y  =  -3.

Solution :

Because the given line is in the form of y = a constant, it remembers the word (HOY). From this, we can come to know the given line is horizontal line. 

So, its slope is zero.

Problem 2 :

Find the slope of the line x  =  5.

Solution :

Because the given line is in the form of x = a constant, it remembers the word (VUX). From this, we can come to know that the given line is vertical line. 

So, its slope is undefined.

Problem 3 :

Find which of the following lines are horizontal lines and also write the equations of those lines.

Solution :

The lines which are parallel to x-axis is known as horizontal lines.

In the above graph, the lines 1, 2, 3 and 4 are parallel to x-axis. 

So, the lines 1, 2, 3 and 4 are horizontal lines. 

Equation of line 1 :

y  =  5

Equation of line 2 :

y  =  2

Equation of line 3 :

y  =  -1

Equation of line 4 :

y  =  -2

Problem 4 :

Check whether x  =  -2 is a horizontal or vertical line ?

Solution : 

Graph x  =  -2 in xy-plane. 

From the above graph, x  =  -2 is a vertical line. 

Problem 5 :

What is the equation of a line that passes through the point (3, -5) and has undefined slope ?

Solution :

Because the slope of the line passes which through the point (3, -5) is undefined, the line has to be a vertical line.

This remembers the word "VUX".  

Then, the equation is in the form x  =  a.

'x  =  a' passes through the point (3, -5). 

So, equation of the required line is x = 3.

Problem 6 :

What is the equation of the line that has zero slope and passes through the point (-2, -5) ?

Solution :

Because the slope of the required line is 0, the line has to be an horizontal line.

This remembers the word "HOY".  

Then, the equation will be in the form of y  =  a.

'y  =  a' passes through the point (-2, -5). 

So, equation of the required line is y  =  -5.

Problem 7 :

What is the slope of the line parallel to y  =  -8 ? 

Solution :

y  =  -8 is an horizontal line.

The line which is parallel to y = -8 must also be an horizontal line. 

So, its slope is zero.

Problem 8 :

What is the slope of the line parallel to x  =  1 ? 

Solution :

x  =  1 is a vertical line.

The line which is parallel to x  =  1 must also be a vertical  line. 

So, its slope is undefined.

Problem 9 :

What is the slope of the line x  =  0 ? 

Solution :

x  =  0 is nothing but y-axis. 

y-axis is a vertical line.

So, its slope is undefined.

Problem 10 :

What is the slope of the line y  =  0 ? 

Solution :

y  =  0 is nothing but x-axis. 

x-axis is an horizontal.

So, its slope is zero. 

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