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

?

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

?

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.

(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?

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

?

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:

?

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:

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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