ACT Math aid » Algebra » Coordinate aircraft » lines » Perpendicular present » exactly how to uncover the equation that a perpendicular line
Explanation:

Convert the equation to steep intercept type to acquire y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes need to be the contrary reciprocals of every other: m1 * m2 = –1

With the new slope, usage the slope intercept kind and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, therefore b = 2

So y = 3x + 2


What heat is perpendicular come

*
and passes v
*
?


*


*


*


*


Explanation:

Convert the given equation to slope-intercept form.

You are watching: Which equation represents a line that passes through (–9, –3) and has a slope of –6?

*

*

*

The slope of this line is

*
. The slope of the heat perpendicular come this one will have a slope same to the an unfavorable reciprocal.

The perpendicular steep is 

*
.

Plug the brand-new slope and also the given allude into the slope-intercept form to discover the y-intercept.

*

*

*

So the equation of the perpendicular line is

*
.


What is the equation the a line the runs perpendicular come the heat 2x + = 5 and also passes with the suggest (2,7)?


Explanation:

First, put the equation that the line given into slope-intercept kind by resolving for y. You gain y = -2x +5, therefore the steep is –2. Perpendicular lines have actually opposite-reciprocal slopes, therefore the slope of the heat we want to uncover is 1/2. Plugging in the point given right into the equation y = 1/2x + b and also solving for b, we get b = 6. Thus, the equation the the heat is y = ½x + 6. Rearranged, it is –x/2 + y = 6.


Line m passes with the clues (1, 4) and (5, 2). If heat p is perpendicular come m, then which of the following could represent the equation for p?


Explanation:

The slope of m is equal to   y2-y1/x2-x1 = 2-4/5-1 = -1/2

Since heat p is perpendicular to heat m, this means that the commodities of the slopes that p and also m need to be 1:

 

(slope the p) * (-1/2) = -1

Slope of p = 2

So us must choose the equation that has a slope of 2. If us rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x  y = 3 could be created as y = 2x – 3. This means that the steep of the heat 2x – y =3 would certainly be 2, so it could be the equation of line p. The prize is 2x – y = 3.


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Example question #5 : how To discover The Equation of A Perpendicular line


What is the equation because that the line the is perpendicular to  through allude

*
?


Possible Answers:
Correct answer:

*


Explanation:

Perpendicular slopes are opposite reciprocals.

The given slope is found by converting the equation to the slope-intercept form.

*
 

The slope of the offered line is

*
and the perpendicular steep is
*
.

We can use the given allude and the new slope to discover the perpendicular equation. Plug in the slope and also the given coordinates to settle for the y-intercept.

*

*

Using this y-intercept in slope-intercept form, we get out last equation:

*
.


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Example concern #1 : exactly how To uncover The Equation of A Perpendicular line


Which line listed below is perpendicular come

*
?


Possible Answers:
Correct answer:

*


Explanation:

The an interpretation of a perpendicular heat is one that has actually a negative, mutual slope to another.

For this specific problem, we must first manipulate our initial equation into a much more easily recognizable and also useful form: slope-intercept type or

*
.

*

*

*

According to our 

*
formula, our slope for the initial line is
*
. We are looking for response that has actually a perpendicular slope, or an the opposite reciprocal. The opposite reciprocal of 
*
is
*
. Upper and lower reversal the original and multiply the by
*

Our answer will have actually a steep of

*
. Search the answer selections for 
*
in the 
*
place of the
*
equation.

*
is our answer. 

(As one aside, the an adverse reciprocal the 4 is

*
. Ar the entirety number end one and also then flip/negate. This walk not apply to the over problem, however should be interpreted to tackle certain permutations that this problem form where the original slope is one integer.)


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Example concern #1 : just how To discover The Equation of A Perpendicular heat


If a line has actually an equation of 

*
, what is the steep of a line that is perpendicular to the line?


Possible Answers:
Correct answer:

*


Explanation:

Putting the an initial equation in slope-intercept form yields

*
.

A perpendicular line has a slope that is the negative inverse. In this case,

*
.


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Example inquiry #8 : how To discover The Equation the A Perpendicular line


Which the the complying with is perhaps a line perpendicular to 

*
?


Possible Answers:
Correct answer:

*


Explanation:

To start, start by dividing everything by 

*
, this will get your equation into the format 
*
. This provides you:

*

Now, recall that the steep of a perpendicular line is the opposite and reciprocal slope to its mutually perpendicular line. Thus, if our slope is 

*
, climate the perpendicular line"s slope must be 
*
. Thus, we should look in ~ our answers to recognize which equation has a slope of 
*
. Amongst the choices given, the only one the matches this is 
*
. If you fix this for 
*
, you will certainly get:

*


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Example question #9 : how To discover The Equation of A Perpendicular heat


Which of the following is the equation of a line perpendicular come the line offered by:

*
?


Possible Answers:
Correct answer:

*


Explanation:

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

*
.
*
 and so we check out the correct answer is given by 
*


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Example inquiry #1 : exactly how To find The Equation of A Perpendicular heat


What is the equation that a line perpendicular to the line identified by the equaiton:


Possible Answers:
Correct answer:

*


Explanation:

Perpendicular lines have actually slopes whose product is 

*
.

Looking at our equations we have the right to see that it is in slope-intercept form where the m value represents the steep of the line,

*
.

In our instance we see that

 therefore, 

*
.

Since 

*
 we check out the only possible answer is 

*
.

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