act Math aid » Algebra » Coordinate airplane » lines » Perpendicular present » exactly how to find the equation the a perpendicular heat
Explanation:

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

With the brand-new slope, use the slope intercept form and the allude to calculation the intercept: y = mx + b or 5 = 3(1) + b, therefore b = 2

So y = 3x + 2

What line is perpendicular come and passes v ?    Explanation:

Convert the provided equation come slope-intercept form.

You are watching: Find the perpendicular slope of the line 3x-9y=15   The steep of this line is . The steep of the line perpendicular come this one will have a slope same to the negative reciprocal.

The perpendicular slope is .

Plug the new slope and the given allude into the slope-intercept type to discover the y-intercept.   So the equation of the perpendicular line is .

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

Explanation:

First, placed the equation of the line provided into slope-intercept form by addressing for y. You gain y = -2x +5, therefore the steep is –2. Perpendicular lines have opposite-reciprocal slopes, for this reason the slope of the line we desire to find is 1/2. Plugging in the allude given right into the equation y = 1/2x + b and solving for b, we gain b = 6. Thus, the equation the 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 line p is perpendicular come m, then which of the following could represent the equation because that p?

Explanation:

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

Since heat p is perpendicular to line m, this method that the products of the slopes that p and also m need to be 1:

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

Slope the p = 2

So us must pick the equation that has actually a slope of 2. If us rewrite the equations in point-slope type (y = mx + b), we see that the equation 2x  y = 3 could be written as y = 2x – 3. This method that the slope of the line 2x – y =3 would be 2, so it might be the equation of line p. The answer is 2x – y = 3.

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### Example inquiry #5 : just how To uncover The Equation the A Perpendicular line

What is the equation because that the line the is perpendicular to  through point ? Explanation:

Perpendicular slopes space opposite reciprocals.

The given slope is uncovered by converting the equation to the slope-intercept form. The steep of the offered line is and the perpendicular slope is .

We deserve to use the given allude and the brand-new slope to find the perpendicular equation. Plug in the slope and the given works with to deal with for the y-intercept.  Using this y-intercept in slope-intercept form, we acquire out final equation: .

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### Example question #1 : just how To find The Equation the A Perpendicular line

Which line below is perpendicular come ? Explanation:

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

For this specific problem, us must first manipulate our initial equation right into a much more easily recognizable and also useful form: slope-intercept form or .   According come our formula, our slope because that the original line is . We room looking for response that has a perpendicular slope, or an the opposite reciprocal. The opposite reciprocal of is . Upper and lower reversal the original and also multiply that by Our price will have a slope of . Search the answer selections for in the position of the equation. (As an aside, the an adverse reciprocal of 4 is . Place the whole number end one and then flip/negate. This walk not use to the above problem, however should be taken to tackle certain permutations the this problem type where the original slope is one integer.)

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### Example inquiry #1 : just how To find The Equation the A Perpendicular heat

If a line has actually an equation of , what is the steep of a line the is perpendicular come the line? Explanation:

Putting the first equation in slope-intercept kind yields .

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

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### Example inquiry #8 : exactly how To uncover The Equation the A Perpendicular heat

Which that the following is probably a heat perpendicular to ? Explanation:

To start, start by splitting everything by , this will obtain your equation into the format . This gives you: Now, recall the the steep of a perpendicular line is the opposite and reciprocal steep to its support perpendicular line. Thus, if our slope is , climate the perpendicular line"s slope must be . Thus, we must look in ~ our answer to recognize which equation has actually a slope of . Among the choices given, the only one the matches this is . If you settle this for , you will certainly get: Report an Error

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

Which the the adhering to is the equation that a line perpendicular to the line given by: ? Explanation:

For two lines to it is in perpendicular their slopes must have actually a product of . and therefore we view the correct answer is offered by Report an Error

### Example concern #10 : how To discover The Equation that A Perpendicular heat

What is the equation of a line perpendicular to the line defined by the equaiton: Explanation:

Perpendicular lines have actually slopes who product is .

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

In our situation we watch that

therefore, .

Since we check out the only possible answer is .

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