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

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

With the new slope, use the slope intercept kind and the allude 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 also passes through
*
?


*


*


*


*


Explanation:

Convert the provided equation come slope-intercept form.

You are watching: Which of the following lines is perpendicular to y=-2x+3

*

*

*

The steep of this heat is

*
. The steep of the heat perpendicular come this one will have actually a slope equal to the negative reciprocal.

The perpendicular slope is 

*
.

Plug the new slope and also the given suggest into the slope-intercept form to find the y-intercept.

*

*

*

So the equation that the perpendicular line is

*
.


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


Explanation:

First, put the equation the the line given into slope-intercept type by fixing for y. You gain y = -2x +5, so the slope is –2. Perpendicular lines have actually opposite-reciprocal slopes, so the steep of the line we want to uncover is 1/2. Plugging in the suggest given right into the equation y = 1/2x + b and solving because that b, we acquire b = 6. Thus, the equation that the line is y = ½x + 6. Rearranged, the is –x/2 + y = 6.


Line m passes v the clues (1, 4) and also (5, 2). If heat p is perpendicular to m, then i beg your pardon of the following might represent the equation for p?


Explanation:

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

Since line p is perpendicular to line m, this method that the commodities of the slopes the p and also m have to be 1:

 

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

Slope that p = 2

So we must choose the equation that has actually a steep of 2. If we rewrite the equations in point-slope kind (y = mx + b), we view that the equation 2x  y = 3 might be created as y = 2x – 3. This method that the steep of the heat 2x – y =3 would certainly be 2, therefore it could be the equation of line p. The price is 2x – y = 3.


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Example concern #5 : how To find The Equation of A Perpendicular line


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

*
?


Possible Answers:
Correct answer:

*


Explanation:

Perpendicular slopes space opposite reciprocals.

The offered slope is discovered by convert the equation come the slope-intercept form.

*
 

The steep of the offered line is

*
and also the perpendicular slope is
*
.

We can use the given point and the brand-new slope to uncover the perpendicular equation. Plugin the slope and the given collaborates to resolve for the y-intercept.

*

*

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

*
.


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Example inquiry #6 : exactly how To uncover The Equation that A Perpendicular line


Which line below is perpendicular come

*
?


Possible Answers:
Correct answer:

*


Explanation:

The meaning of a perpendicular heat is one that has actually a negative, reciprocal slope come another.

For this certain problem, us must an initial manipulate our initial equation right into a much more easily recognizable and useful form: slope-intercept form or

*
.

*

*

*

According to our 

*
formula, our slope because that the original line is
*
. We room looking for an answer that has actually a perpendicular slope, or an the opposite reciprocal. The opposite reciprocal of 
*
is
*
. Flip the original and multiply the by
*

Our prize will have actually a steep of

*
. Find the answer options for 
*
in the 
*
place of the
*
equation.

*
is our answer. 

(As an aside, the negative reciprocal that 4 is

*
. Location the entirety number over one and then flip/negate. This go not apply to the above problem, however should be interpreted to tackle details permutations of this problem type where the initial slope is an integer.)


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Example question #7 : just how To discover The Equation the A Perpendicular heat


If a line has actually an equation of 

*
, what is the slope of a line that is perpendicular come the line?


Possible Answers:
Correct answer:

*


Explanation:

Putting the first equation in slope-intercept type yields

*
.

A perpendicular line has actually a slope the is the an adverse inverse. In this case,

*
.


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Example question #8 : exactly how To uncover The Equation the A Perpendicular line


Which of the following is probably a line perpendicular to 

*
?


Possible Answers:
Correct answer:

*


Explanation:

To start, begin by splitting everything by 

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

*

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

*
, then the perpendicular line"s slope must be 
*
. Thus, we have to look in ~ our answer to recognize which equation has a slope of 
*
. Amongst the alternatives given, the only one the matches this is 
*
. If you solve this for 
*
, you will get:

*


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Example concern #9 : exactly how To discover The Equation that A Perpendicular line


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

*
?


Possible Answers:
Correct answer:

*


Explanation:

For two lines to it is in perpendicular their slopes must have actually a product of 

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


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


What is the equation that a line perpendicular come the line characterized by the equaiton:


Possible Answers:
Correct answer:

*


Explanation:

Perpendicular lines have slopes whose product is 

*
.

Looking in ~ our equations we deserve to see that it is in slope-intercept kind where the m value represents the steep of the line,

*
.

In our case we see that

 therefore, 

*
.

Since 

*
 we watch the only possible answer is 

*
.

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