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Example Questions
Example Question #11 : How To Find The Equation Of A Perpendicular Line
Write the equation of a line passing through the point that is perpendicular to the line
.
To solve this type of problem, we have to be familiar with the slope-intercept form of a line, where m is the slope and b is the y-intercept. The line that our line is perpendicular to has the slope-intercept equation
, which means that the slope is
.
The slope of a perpendicular line would be the negative reciprocal, so our slope is .
We don't know the y-intercept of our line yet, so we can only write the equation as:
.
We do know that the point is on this line, so to solve for b we can plug in -2 for x and 3 for y:
First we can multiply
to get
.
This makes our equation now:
either by subtracting 3 from both sides, or just by looking at this critically, we can see that b = 0.
Our original becomes
, or simply
.
Example Question #81 : Perpendicular Lines
Write the equation of a line perpendicular to
None of the other answers.
Two lines are perpendicular if and only if their slopes are "negative reciprocals" of each other such as 1/2 and -2. In our problem we are not given line equations that we can readily see the slope, so we must convert each equation to slope intercept form or .
First find out the slope of the given equation by converting it to slope-intercept form:
So we need a line whose slope is the negative reciprocal of -1/8 (which is 8). Even though this number is not "negative" the idea of the negative reicprocal gives a positive number here because two negative signs cancel each other to make a positive. ...negative recicprocal...
.
Now we must choose an equation that, after being changed to slope intercept form has a slope of 8.
So (answer) is the equation of a line that is perpendicular to
.
Example Question #83 : Perpendicular Lines
What is a line that is perpendicular to ?
A line is perpendicular to another line when they meet at a degree angle. That angle is the result of the slopes of the lines being opposite reciprocals.
The "opposite reciprocal" of is best described as
.
First we reorganize the original equation to isolate . To do this we want to get our equation into slope intercept form
.
First subtract 12 from each side.
Now divide by 4 and simplify where possible.
opposite reciprocal
The only equation in the answer choices with a slope of is
.
Example Question #84 : Perpendicular Lines
A line perpendicular to passes through the points
and
. Find the equation of this line.
This problem can be quickly solved through using the point-slope formula considering the given information. Before we start substituting in values, however, it's important to remember what determines a line to be perpendicular relative to another. By definition, lines are perpendicular if their slopes have a product of . For instance, if a line has a slope of
, the line perpendicular to it will have a slope of
because
. Using this concept, we must first determine the slope of the perpendicular line. We are given that the reference line has a slope of
. That means the perpendicular line must have a slope of
because
. Now that we know
(slope) and have a coordinate, we have fulfilled the requirements of the point-slope formula and can begin to substitue in information and solve for the equation.
Here we arbitrarily use
Example Question #85 : Perpendicular Lines
A line has a y-intercept of 7 and is perpendicular to a line with a slope of . What is the equation of this perpendicular line?
Before beginning this problem, it's important to remember what defines a perpendicular line. A line is perpendicular to another if the product of the two lines' slope is For instance, if a line has a slope of
, the line perpendicular to it will have a slope of
because
. Using this concept, we must first determine the slope of the perpendicular line. The line of interest is perpendicular to a line with a slope of
, therefore its slope must be
The problem does not provide us enough information to use the point-slope formula to solve for the equation. However, we are provided with the line's y-intercept. This allows us to use the skeleton to solve for the equation, where
is slope and
is the y-intercept.
Example Question #86 : Perpendicular Lines
A line is perpendicular to and has a y-intercept of
. Find the equation of this perpendicular line.
By definition, lines are perpendicular if the product of their slopes is . For example, if a line has a slope of
, the perpendicular line would have a slope of
. This same concept can be used to solve this problem. Beginning with the issue of slope, we realize that the reference slope is
. In order to create a product of
, we must multiply
by
. Therefore, the slope of the perpendicular line is
.
Because the problem has not given us a point, we cannot use the point-slope formula to solve for the equation. However, we have been provided with the line's y-intercept. With this information, we are ready to construct the line's equation remembering the skeleton. We have
and now we have
. Substituting in the given information will yield our answer.
Because is usally not written in front of variables, we may omit it from the final answer.
Example Question #331 : Functions And Lines
Line 1 passes through points (0,2) and (3,3). Line 2 is perpindicular to Line 1. Also, Line 2 passes through the point (8,5). Which of the following represents the equation of Line 2?
Begin by calculating the slope of Line 1 as
.
Now, realize that since Line 2 is perpindicular to Line 1, the slope of Line 2 is the negative reciprocal of the slope of Line 1.
Therefore, the slope of Line 2 is given as
.
We also know that Line 2 passes through point (8,5).
Therefore, we may use "point-slope" form to express the equation of Line 2 as:
.
Finally, convert this "point-slope" equation to "slope-intercept" form in order to match the result with the correct answer choice:
.
Example Question #82 : Perpendicular Lines
What is the equation of a line that is perpendicular to and passes through point
?
When finding the slope of a perpendicular line, we need to ensure we have form.
stands for slope. Our
is
. To find the perpendicular slope, we need to take the negative reciprocal of that value which is
. Since we are looking for an equation, we need to reuse the
form to solve for
. We do this by plugging in our coordinates.
Add
on both sides.
Our equation is now .
Example Question #89 : Perpendicular Lines
What's the equation of a line that is perpendicular to and passes through point
?
When finding the slope of a perpendicular line, we need to ensure we have form. Let's rearrange it. By subtracting
on both sides and dividing
on both sides, we get
.
stands for slope. Our
is
. To find the perpendicular slope, we need to take the negative reciprocal of that value which is
. Since we are looking for an equation, we need to reuse the
form to solve for
. We do this by plugging in our coordinates.
Subtract
on both sides.
Our equation is now .
Example Question #90 : Perpendicular Lines
What's the equation of a line that is perpendicular to and goes through point
?
When finding the slope of a perpendicular line, we need to ensure we have form. Let's rearrange it. By add
on both sides and dividing
on both sides, we get
.
stands for slope. Our
is
. To find the perpendicular slope, we need to take the negative reciprocal of that value which is
. Since we are looking for an equation, we need to reuse the
form to solve for
. We do this by plugging in our coordinates.
Add
on both sides.
Our equation is now .
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