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 ? 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 ? 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. (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? 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 ? 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: Report an Error

### 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: ? 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 Report one Error

### 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: 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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