Straight lines  product of slope of perpendicular lines.
As per wikipedia
"Two lines are parallel if and only if their slopes are equal and they are not the same line (coincident) or if they both are vertical and therefore both have undefined slopes. Two lines are perpendicular if the product of their slopes is −1 or one has a slope of 0 (a horizontal line) and the other has an undefined slope (a vertical line)."
So, it is obvious that the rule of multiplication of slopes is not applied when one of the line is vertical and another horizontal. Further, yaxis (or more specifically, the line x = 0) doesn't have a slope of infinity but it is undefined.
answered Dec 19 '16 at
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Parallel & Perpendicular Lines
Purplemath
Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
Perpendicular lines are a bit more complicated.
If you visualize a line with positive slope (so it's an increasing line), then the perpendicular line must have negative slope (because it will have to be a decreasing line). So perpendicular lines have slopes which have opposite signs.
MathHelp.com
The other "opposite" thing with perpendicular slopes is that their values are reciprocals; that is, you take the one slope value, and flip it upside down. (This is the nonobvious thing about the slopes of perpendicular lines.) Put this together with the sign change, and you get that the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other.
To give a numerical example of "negative reciprocals", if the one line's slope is , then the perpendicular line's slope will be . Or, if the one line's slope is m = –2, then the perpendicular line's slope will be . (Remember that any integer can be turned into a fraction by putting it over 1.)
In your homework, you will probably be given some pairs of points, and be asked to state whether the lines through the pairs of points are "parallel, perpendicular, or neither". To answer the question, you'll have to calculate the slopes and compare them. Here's how that works:
One line passes through the points (–1, –2) and (1, 2); another line passes through the points (–2, 0) and (0, 4). Are these lines parallel, perpendicular, or neither?
To answer this question, I'll find the two slopes. So I can keep things straight and tell the difference between the two slopes, I'll use subscripts.
Since these two lines have identical slopes, then:
these lines are parallel.
One line passes through the points (0, –4) and (–1, –7); another line passes through the points (3, 0) and (–3, 2). Are these lines parallel, perpendicular, or neither?
I'll find the values of the slopes.
If I were to convert the "3" to fractional form by putting it over "1", then flip it and change its sign, I would get " . This negative reciprocal of the first slope matches the value of the second slope. In other words, these slopes are negative reciprocals, so:
the lines are perpendicular.
One line passes through the points (–4, 2) and (0, 3); another line passes through the points (–3, –2) and (3, 2). Are these lines parallel, perpendicular, or neither?
I'll find the slopes.
These slope values are not the same, so the lines are not parallel. The slope values are also not negative reciprocals, so the lines are not perpendicular. Then the answer is:
Find the slope of a line perpendicular to the line y = –4x + 9.
They've given me the original line's equation, and it's in "y=" form, so it's easy to find the slope. I can just read the value off the equation: m = –4.
This slope can be turned into a fraction by putting it over 1, so this slope can be restated as:
To get the negative reciprocal, I need to flip this fraction, and change the sign. Then the slope of any line perpendicular to the given line is:
Warning: When asked a question of this type ("are these lines parallel or perpendicular?"), do not start drawing pictures. If the lines are close to being parallel or close to being perpendicular (or if you draw the lines messily), you can veryeasily get the wrong answer from your picture.
Besides, they're not asking if the lines look parallel or perpendicular; they're asking if the lines actually are parallel or perpendicular. The only way to be sure of your answer is to do the algebra.
URL: https://www.purplemath.com/modules/slope3.htm
Intermediate Algebra Tutorial The Slope of a Line 
WTAMU> Virtual Math Lab > Intermediate Algebra
Learning Objectives
After completing this tutorial, you should be able to:

Introduction
This tutorial takes us a little deeper into linear equations. We will be looking at the slope of a line. We will also look at the relationship between the slopes of parallel lines as well as perpendicular lines. Let's see what you can do with slopes. 
Tutorial
The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run".
Here are some visuals to help you with this definition: Positive slope: Note that when a line has a positive slope it goes up left to right. 
Negative slope: Note that when a line has a negative slope it goes down left to right. 
Zero slope: slope = 0 Note that when a line is horizontal the slope is 0. 
Undefined slope: slope = undefined Note that when the line is vertical the slope is undefined. 
Given two points and 
The subscripts just indicate that these are two different points. It doesn't matter which one you call point 1 and which one you call point 2 as long as you are consistent throughout that problem. Note that we use the letter m to represent slope. Example 1: Find the slope of the straight line that passes through (5, 2) and (4, 7). 
*Simplify

Make sure that you are careful when one of your values is negative and you have to subtract it as we did in line 2. 4  (5) is not the same as 4  5. The slope of the line is 
Example 2: Find the slope of the straight line that passes through (1, 1) and (5, 1). 
*Plug in x and y values into slope formula *Simplify

It is ok to have a 0 in the numerator. Remember that 0 divided by any nonzero number is 0. The slope of the line is 0. 
Example 3: Find the slope of the straight line that passes through (3, 4) and (3, 6). 
*Plug in x and y values into slope formula *Simplify

Since we did not have a change in the x values, the denominator of our slope became 0. This means that we have an undefined slope. If you were to graph the line, it would be a vertical line, as shown above. The slope of the line is undefined. 
If your linear equation is written in this form, m represents the slope and b represents the yintercept. This form can be handy if you need to find the slope of a line given the equation. 
Slope/Intercept Equation of a Line 
m still represents slope and b still represents the yintercept. 
Example 4: Find the slope and the yintercept of the line . 
As mentioned above, if the equation is in the slope/intercept form, we can easily see what the slope and yintercept are. Let&#;s go ahead and get it into the slope/intercept form first: 
*Inverse of mult. by 3 is div. by 3 *Written in slope/intercept form 
Lining up the form with the equation we got, can you see what the slope and yintercept are? In this form, the slope is m, which is the number in front of x. In our problem, that would have to be In this form, the yintercept is b, which is the constant. In our problem, that would be 2. The answer is the slope is 1 and the yintercept is 2. 
Example 5: Find the slope and the yintercept of the line . 
This example is written in function notation, but is still linear. As shown above, you can still read off the slope and intercept from this way of writing it. In this example, it is already written in the slope/intercept form, so we do not have to mess around with it. We can get down to business and answer our question of what are the slope and yintercept. 

Lining up the form with the equation we got, can you see what the slope and yintercept are? In this form, the slope is m, which is the number in front of x. In our problem, that would have to be 2. In this form, the yintercept is b, which is the constant. In our problem, that would be The answer is the slope is 2 and the yintercept is 
Example 6: Find the slope and the yintercept of the line x= 5. 
Note how we do not have a y. This type of linear equation was shown in Tutorial Graphing Linear Equations. When we have x = c, where c is a constant, then this graph is what type of line? Since this is a special type of linear equation that can&#;t be written in the slope/intercept form, I&#;m going to give you a visual of what is happening and then from that let&#;s see if we can&#;t figure out the slope and yintercept. The graph would look like this: 
First, let&#;s talk about the slope. Note that all the x values on this graph are 5. That means the change in x, which is the denominator of the slope formula, would be 5  5 = 0. Well you know that having a 0 in the denominator is a big no, no. This means the slope is undefined. As shown above, whenever you have a vertical line your slope is undefined. Now let&#;s look at the yintercept. Looking at the graph, you can see that this graph never crosses the yaxis, therefore there is no yintercept either. Another way to look at this is the x value has to be 0 when looking for the yintercept and in this problem x is always 5. So, for all our efforts on this problem, we find that the slope is undefined and the yintercept does not exist. 
Example 7: Find the slope and the yintercept of the line y= 
Note how we do not have an x. This type of linear equation was shown in Tutorial Graphing Linear Equations. When we have y = c, where c is a constant, then this graph is what type of line? Since this is a special type of linear equation that can&#;t be written in the slope/intercept form, I&#;m going to give you a visual of what is happening and then from that let&#;s see if we can&#;t figure out the slope and yintercept. The graph would look like this: 
First, let&#;s talk about the slope. Note how all of the y values on this graph are That means the change in y, which is the numerator of the slope formula would be 2  (2) = 0. Having 0 in the numerator and a nonzero number in the denominator means only one thing. The slope equals 0. Now let&#;s look at the yintercept. Looking at the graph, you can see that this graph crosses the yaxis at (0, 2). So the yintercept is (0, 2). The slope is 0 and the yintercept is 
In other words, the slopes of parallel lines are equal. Note that two lines are parallel if there slopes are equal and they have different yintercepts. 
In other words, perpendicular slopes are negative reciprocals of each other. 
Example 8: Determine if the lines are parallel, perpendicular, or neither. and . 
In order for these lines to be parallel their slopes would have to be equal and to be perpendicular they would have to be negative reciprocals of each other. So let&#;s find out what the slopes are. Since the equations are already in the slope/intercept form, we can look at them and see the relationship between the slopes. What do you think? The slope of the first equation is 7 and the slope of the second equation is 7. Since the two slopes are equal and their yintercepts are different, the two lines would have to be parallel. 
Example 9: Determine if the lines are parallel, perpendicular, or neither. and . 
Again, the equations are already in the slope/intercept form, so let&#;s go right to looking for the slope. What did you find? I found that the slope of the first equation is 4 and the slope of the second equation is 1/4. So what does that mean? Since the two slopes are negative reciprocals of each other, the two lines would be perpendicular to each other. 
Example 10: Determine if the lines are parallel, perpendicular, or neither. and . 
Writing the first equation in the slope/intercept form we get: 

Writing the second equation in the slope/intercept form we get: 
*Inverse of mult. by 2 is div. by 2 *Written in slope/intercept form 
In order for these lines to be parallel their slopes would have to be equal and to be perpendicular they would have to be negative reciprocals of each other. So let&#;s find out what the slopes are. Since the equations are now in the slope/intercept form, we can look at them and see the relationship between the slopes. What do you think? The slope of the first equation is and the slope of the second equation is Since the two slopes are not equal and are not negative reciprocals of each other, then the answer would be neither. 
Practice Problems
These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice. To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer. 
Practice Problem 1a  1b: Find the slope of the straight line that passes through the given points.
Practice Problems 2a  2c: Find the slope and the yintercept of the line.
Practice Problems 3a  3b: Determine if the lines are parallel, perpendicular, or neither.
Practice Problem 4a: Determine the slope of the line.
Need Extra Help on these Topics?
WTAMU> Virtual Math Lab > Intermediate Algebra
Last revised on July 3, by Kim Seward.
All contents copyright (C)  , WTAMU and Kim Seward. All rights reserved.
SlopeIntercept Form
Linear functions are graphically represented by lines and symbolically written in slopeintercept form as,
y = mx + b,
where m is the slope of the line, and b is theyintercept. We call b the yintercept because the graph of y = mx + b intersects the yaxis at the point (0, b). We can verify this by substituting x = 0 into the equation as,
y = m · 0 + b = b.
Notice that we substitute x = 0 to determine where a function intersects the yaxis because the xcoordinate of a point lying on the yaxis must be zero.
The Definition of Slope :
The constant m expressed in the slopeintercept form of a line, y = mx + b, is the slope of the line. Slope is defined as the ratio of the rise of the line (i.e. how much the line rises vertically) to the run of line (i.e. how much the line runs horizontally).
Definition For any two distinct points on a line, (x_{1}, y_{1}) and (x_{2}, y_{2}), the slope is,

Intuitively, we can think of the slope as measuring the steepness of a line. The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y_{1} − y_{2} = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x_{1} − x_{2} = 0).
Zero and Undefined Slope
As stated above, horizontal lines have slope equal to zero. This does not mean that horizontal lines have no slope. Since m = 0 in the case of horizontal lines, they are symbolically represented by the equation, y = b. Functions represented by horizontal lines are often called constant functions. Vertical lines have undefined slope. Since any two points on a vertical line have the same xcoordinate, slope cannot be computed as a finite number according to the formula,
because division by zero is an undefined operation. Vertical lines are symbolically represented by the equation, x = a where a is the xintercept. Vertical lines are not functions; they do not pass the vertical line test at the point x = a.
Positive Slopes
Lines in slopeintercept form with m > 0 have positive slope. This means for each unit increase in x, there is a corresponding m unit increase in y (i.e. the line rises by m units). Lines with positive slope rise to the right on a graph as shown in the following picture,
Lines with greater slopes rise more steeply. For a one unit increment in x, a line with slope
m_{1} = 1 rises one unit while a line with slope m_{2} = 2 rises two units as depicted,
Negative Slopes
Lines in slopeintercept form with m < 0 have negative slope. This means for each unit increase in x, there is a corresponding m unit decrease in y (i.e. the line falls by m units). Lines with negative slope fall to the right on a graph as shown in the following picture,
The steepness of lines with negative slope can also be compared. Specifically, if two lines have negative slope, the line whose slope has greatest magnitude (known as the absolute value) falls more steeply. For a one unit increment in x, a line with slope m_{3} = −1 falls one unit while a line with slope m_{4}= −2 falls two units as depicted,
Parallel and Perpendicular Lines
Two lines in the xyplane may be classified as parallel or perpendicular based on their slope. Parallel and perpendicular lines have very special geometric arrangements; most pairs of lines are neither parallel nor perpendicular. Parallel lines have the same slope. For example, the lines given by the equations,
y_{1} = −3x + 1,
y_{2} = −3x − 4,
are parallel to one another. These two lines have different yintercepts and will therefore never intersect one another since they are changing at the same rate (both lines fall 3 units for each unit increase in x). The graphs of y_{1} and y_{2} are provided below,
Perpendicular lines have slopes that are negative reciprocals of one another. In other words, if a line has slope m_{1}, a line that is perpendicular to it will have slope,
An example of two lines that are perpendicular is given by the following,
These two lines intersect one another and form ninety degree (90°) angles at the point of intersection. The graphs of y_{3} and y_{4} are provided below,
*****
In the next section we will describe how to solve linear equations.
Linear equations
0 of perpendicular slope
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How do you find the slope of a line perpendicular to another line?
How do you find the slope of a line perpendicular to another line?
To find the slope of the given line we need to get the line into slopeintercept form (y = mx + b), which means we need to solve for y: The slope of the line 4x – 5y = –10 is m = 4/5. Therefore, the slope of the line perpendicular to this line would have to be m = –5/4.
What is the slope of a line perpendicular to this line what is the slope of a line parallel to this line?
Vertical lines and horizontal lines are perpendicular to each other. The slope of the perpendicular line in this case would be the slope of a horizontal line which would be 0. The slope of the parallel line is undefined and the slope of the perpendicular line is 0.
What slope is perpendicular to 8?
Using the slopeintercept form, the slope is Undefined. The slope of a perpendicular line to a vertical line is zero.
What is the slope of a line that is perpendicular to the line shown on the graph 4?
If the line has a slope of 4, then a line perpendicular to it would have a slope of 1/4. If the line has a slope of 4, then a line perpendicular to it would have a slope of 1/4.
Which line is perpendicular to a line that has a slope of 1 3?
The slope of a line perpendicular to one with the slope of 13 is −3 . See explanation.
What is the slope of a line that is perpendicular to the line y x 4 the slope of the line is?
Answer Expert Verified The opposite reciprocal of 1 is 1, thus the slope of a line perpendicular to the line y = x + 4 is Hope this helps.
What is the slope of a line perpendicular to Y = 7 4x?
Using the slopeintercept form, the slope is −74 . The equation of a perpendicular line to y=−7&#;4 y = &#; 7 x 4 must have a slope that is the negative reciprocal of the original slope. Simplify the result. Cancel the common factor of 1 1 and −1 &#; 1 .
What is the slope of a line that is perpendicular to the line y 1 6x 4 the slope of the line is?
The slope would be 6 because it is the opposite reciprocal.
What is the slope of a line that is perpendicular to the line y 2x 1?
Algebra Examples Using the slopeintercept form, the slope is 2 2 .
What is the perpendicular slope of 0?
The slope of a line perpendicular to a line with a slope of 0 is undefined. The perpendicular line is a vertical line. A line with a slope of 0 is a horizontal line.
What happens if the slope of a line is 0?
Since we did not have a change in the x values, the denominator of our slope became 0. This means that we have an undefined slope. If you were to graph the line, it would be a vertical line, as shown above. The slope of the line is undefined.
What does parallel lines look like?
Parallel lines look like railroad tracks: they are always the same distance apart, running next to each other. The lines do intersect. Next, determine if the lines intersect at a right angle. The lines do not intersect at a right angle.
What is the slope of the line 0?
The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0). because division by zero is an undefined operation.
Is a line with a slope of 0 linear?
No, so its slope can&#;t be positive. This relationship always holds: a slope of zero means that the line is horizontal, and a horizontal line means you&#;ll get a slope of zero. (By the way, all horizontal lines are of the form &#;y = some number&#;, and the equation &#;y = some number&#; always graphs as a horizontal line.)
What does a zero slope mean?
A slope of zero means that there is a constant relationship between x and y. Graphically, the line is flat; the rise over run is zero.
What is the slope intercept form if the slope is 0?
y=mx + b When the equation is in this form, the coefficient of x will be the slope and the yintercept will be (0,b). If the denominator of the fraction is 0, the slope is undefined. This occurs if the x value is the same for both points.
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