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Example Questions
Example Question #1 : How To Find The Equation Of A Perpendicular Line
What line is perpendicular to x + 3y = 6 and travels through point (1,5)?
y = 2x + 1
y = 2/3x + 6
y = 3x + 2
y = 6x – 3
y = –1/3x – 4
y = 3x + 2
Convert the equation to slope intercept form to get y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3x + 2
Example Question #1 : How To Find The Equation Of A Perpendicular Line
What line is perpendicular to and passes through
?
Convert the given equation to slope-intercept form.
The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
The perpendicular slope is .
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is .
Example Question #1 : How To Find The Equation Of A Perpendicular Line
What is the equation of a line that runs perpendicular to the line 2x + y = 5 and passes through the point (2,7)?
2x – y = 6
–x/2 + y = 6
2x + y = 7
x/2 + y = 5
x/2 – y = 6
–x/2 + y = 6
First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.
Example Question #1 : How To Find The Equation Of A Perpendicular Line
Line m passes through the points (1, 4) and (5, 2). If line p is perpendicular to m, then which of the following could represent the equation for p?
4x – 3y = 4
3x + 2y = 4
2x + y = 3
2x – y = 3
x – y = 3
2x – y = 3
The slope of m is equal to y2-y1/x2-x1 = 2-4/5-1 = -1/2
Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be –1:
(slope of p) * (-1/2) = -1
Slope of p = 2
So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.
Example Question #1 : How To Find The Equation Of A Perpendicular Line
What is the equation for the line that is perpendicular to through point
?
Perpendicular slopes are opposite reciprocals.
The given slope is found by converting the equation to the slope-intercept form.
The slope of the given line is and the perpendicular slope is
.
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.
Using this y-intercept in slope-intercept form, we get out final equation: .
Example Question #1 : How To Find The Equation Of A Perpendicular Line
Which line below is perpendicular to ?
The definition of a perpendicular line is one that has a negative, reciprocal slope to another.
For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or .
According to our formula, our slope for the original line is
. We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal of
is
. Flip the original and multiply it by
.
Our answer will have a slope of . Search the answer choices for
in the
position of the
equation.
is our answer.
(As an aside, the negative reciprocal of 4 is . Place the whole number over one and then flip/negate. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.)
Example Question #7 : How To Find The Equation Of A Perpendicular Line
If a line has an equation of , what is the slope of a line that is perpendicular to the line?
Putting the first equation in slope-intercept form yields .
A perpendicular line has a slope that is the negative inverse. In this case, .
Example Question #8 : How To Find The Equation Of A Perpendicular Line
Which of the following is possibly a line perpendicular to ?
To start, begin by dividing everything by , this will get your equation into the format
. This gives you:
Now, recall that the slope of a perpendicular line is the opposite and reciprocal slope to its mutually perpendicular line. Thus, if our slope is , then the perpendicular line's slope must be
. Thus, we need to look at our answers to determine which equation has a slope of
. Among the options given, the only one that matches this is
. If you solve this for
, you will get:
Example Question #9 : How To Find The Equation Of A Perpendicular Line
Which of the following is the equation of a line perpendicular to the line given by:
?
For two lines to be perpendicular their slopes must have a product of .
and so we see the correct answer is given by
Example Question #10 : How To Find The Equation Of A Perpendicular Line
What is the equation of a line perpendicular to the line defined by the equaiton:
Perpendicular lines have slopes whose product is .
Looking at our equations we can see that it is in slope-intercept form where the m value represents the slope of the line,
.
In our case we see that
therefore,
.
Since
we see the only possible answer is
.
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