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Which the the complying with lines is perpendicular to the line

*
?

 


*


*


*


*


Explanation:

Perpendicular present will have actually slopes that are an unfavorable reciprocals that one another. Our an initial step will be to find the slope of the given line by placing the equation right into slope-intercept form.

You are watching: If two lines are perpendicular, then they form

*

*

The steep of this line is

*
. The an adverse reciprocal will certainly be
*
, which will be the slope of the perpendicular line.

Now we need to find the answer selection with this slope by convert to slope-intercept form.

*

*

*

*

This equation has actually a slope of

*
, and must be our answer.


Explanation:

When identify if a two lines are perpindicular, us are just concerned about their slopes. Take into consideration the an easy equation of a line, 

*
, wherein m is the steep of the line. 2 lines space perpindicular come each various other if one slope is the an adverse and mutual of the other.

The an initial step that this difficulty is to acquire it into the form,

*
, i beg your pardon is 
*
. Now we understand that the slope, m, is 
*
. The mutual of that is 
*
, and the an unfavorable of the is 
*
. Therefore, any kind of line that has actually a slope of 
*
 will be perpindicular come the original line.


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Example inquiry #25 : Perpendicular currently


Which that the following lines is perpendicular to the line v the given equation:

*
?


Possible Answers:
Correct answer:

*


Explanation:

First we have to recognize that the equation is given in slope-intercept form,

*
 where 
*
 is the slope of the line.

Two lines are perpendicular if and also only if the product of their slopes is 

*
. In other words, the steep of a line that is perpendicular to a provided line is the an adverse reciprocal of the slope.

Thus, because that a line with a offered slope that 3, the heat perpendicular to that slope must be the an unfavorable reciprocal of 3, or 

*
.

To twin check that that go indeed give a product of 

*
 when multiplied by three merely compute the product: 

*


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Example question #26 : Perpendicular present


Are the adhering to two currently parallel, perpendicular, or neither:

 and 


Possible Answers:

They space neither perpendicular or parallel.


More info is needed.


They space parallel.


They space perpendicular.


They are both perpendicular and parallel.


Correct answer:

They space perpendicular.


Explanation:

Perpendicular lines have slopes whose product is 

*
.

The steep is regulated by the coefficient,

*
 from the genral kind of the slope-intercept equation: 

*

Thus the two lines room perpendicular because:

 has 

*

and

 has 

*

which as soon as multiplied together results in,

*
.


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Example concern #27 : Perpendicular lines


Are the following two lines perpendicular:

*


Possible Answers:
Correct answer:

*


Explanation:

For two lines to be perpendicular, their slopes have to have a product of 

*
. Uncover the slopes by the coefficient in prior of the
*
.
*
 and so the two lines room perpendicular. The y-intercept does not matter for identify perpendicularity.


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Example inquiry #28 : Perpendicular present


Are the lines explained by the equations 

*
 and 
*
 perpendicular to one another? Why or why not?


Possible Answers:

Yes, because the product of their slopes is

*
.


No, since the product of your slopes is

*
.


Yes, due to the fact that the product of your slopes is not 

*
.


No, due to the fact that the product of your slopes is not .


Correct answer:

No, due to the fact that the product of your slopes is no .


Explanation:

If the slopes of 2 lines can be calculated, an easy way to identify whether they space perpendicular is to multiply their slopes. If the product of the slopes is 

*
, climate the lines are perpendicular.

 

In this case, the steep of the line 

*
 is 
*
 and the steep of the line 
*
 is 
*
.

Since 

*
, the slopes are not perpendicular.


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Example concern #1 : how To uncover Out If Lines are Perpendicular


Line 

*
, which adheres to the equation 
*
, intersects line 
*
 at 
*
. If line 
*
 also passes through 
*
, are 
*
 and 
*
 perpendicular?


Possible Answers:

No, since the product of your slope is not 

*
.


Yes, since the product of your slopes is not 

*
.


No, because the product of their slopes is 

*


Yes, due to the fact that the product of your slopes is .


Correct answer:

Yes, because the product of their slopes is .


Explanation:

The product of perpendicular slopes is always 

*
. Understanding this, and also seeing the the slope of line 
*
 is 
*
, us know any type of perpendicular line will have actually a slope of 
*
.

Since line 

*
 passes through 
*
 and 
*
, we deserve to use the slope equation:

*

Since the two slopes" product is 

*
, the lines room perpendicular.


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Example question #2 : how To discover Out If Lines room Perpendicular


Are the complying with two present perpendicular:

*
 and

*


Possible Answers:
Correct answer:

*


Explanation:

For two lines to be perpendicular they have to have slopes the multiply to get 

*
. The steep is found from the 
*
 in the basic equation: 
*
.

For the an initial line, 

*
 and because that the second 
*
*
 and so the lines are not perpendicular.


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Example question #1 : how To find Out If Lines are Perpendicular


Which that the adhering to equations to represent a line that is perpendicular to the line through points

*
 and
*
?


Possible Answers:
Correct answer:

*


Explanation:

If lines space perpendicular, then their slopes will certainly be an adverse reciprocals.

First, we need to find the slope of the given line.

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*

*

*

*

 

Because we understand that our given line"s steep is

*
, the steep of the heat perpendicular to it need to be 
*
.


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