How to find out if lines are parallel - Algebra
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Which answer choice represents a line that's parallel to the following linear equation?
Which answer choice represents a line that's parallel to the following linear equation?
We are given
and we compare it to the general formula of a straight line
where 
is the slope and 
is the y-intercept. In our case, 
. Know that in order for another function to be parallel, it has to have the same slope. Therefore, we pick an answer choice that has the slope of 
. It turns out that the answer choice is
We are given
and we compare it to the general formula of a straight line
where
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Determine if the lines 
and 
are parallel.
Determine if the lines
Parallel lines need to have slopes that are equal. For the line 
, the slope is 3, since this is the coefficient attached to the x-variable. For the line 
, the slope is 4. Because these slopes are not equal, the lines are not parallel.
Parallel lines need to have slopes that are equal. For the line
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Which of the following lines are parallel to y = 2x + 5?
Which of the following lines are parallel to y = 2x + 5?
Lines are parallel if they have the same slope. The lines are all given in the form y = mx + b. In this form, m represents the slope, thus, we are looking for another line with a slope of 2. This is y = 2x – 3.
Note that the line given by y = (–1/2)x + 6 has a slope that is the negative reciprocal of 2. This line will be perpendicular to our given line.
Lines are parallel if they have the same slope. The lines are all given in the form y = mx + b. In this form, m represents the slope, thus, we are looking for another line with a slope of 2. This is y = 2x – 3.
Note that the line given by y = (–1/2)x + 6 has a slope that is the negative reciprocal of 2. This line will be perpendicular to our given line.
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True or False.
The following two lines are parallel.
True or False.
The following two lines are parallel.
When both equations are solved for the form 
the slopes are the same.
When both equations are solved for the form
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Which of the following lines are parallel to 
?
Which of the following lines are parallel to
Parallel lines must have identical slopes. The given equation is in the 
form. Therefore, we can quickly determine that its slope is 3. The only other equation with a slope of 3 is 
.
Parallel lines must have identical slopes. The given equation is in the
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Which of these lines is parallel to 
?
Which of these lines is parallel to
Parallel lines have the same slope. Since all of these equations are in the 
form, it is easy to determine their slopes, 
. The slope of 
is 2.
The only other line with a slope of 2 is 
.
Parallel lines have the same slope. Since all of these equations are in the
The only other line with a slope of 2 is
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Which of these lines is parallel to 
?
Which of these lines is parallel to
Parallel lines must have equal slopes to one another. Since all of the lines are in the 
form, it is easy to determine their slopes. The given line has a slope of 3, which means that any line that is parallel to it must have a slope of 3. The only other line with a slope of 3 is 
.
Parallel lines must have equal slopes to one another. Since all of the lines are in the
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Which of these pairs of lines are parallel?
Which of these pairs of lines are parallel?
Parallel lines have the same slope as one another. The only pair of lines with the same slope is 
.
Parallel lines have the same slope as one another. The only pair of lines with the same slope is
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Which of the following lines is parallel to the line given by the equation 
?
Which of the following lines is parallel to the line given by the equation
Parallel lines have the same slope. To find the slope of a given equation, it is necessary to convert it to slope-intercept form.
Subtract the 
from both sides.
Divide by 
.
Understanding slope-intercepts form, we can see that the slope is 
.
We can convert each answer choice to slope-intercept form to detrmine which has a slope matching the equation in the question.
This equation has the same slope, and is therefore parallel.
Parallel lines have the same slope. To find the slope of a given equation, it is necessary to convert it to slope-intercept form.
Subtract the
Divide by
Understanding slope-intercepts form, we can see that the slope is
We can convert each answer choice to slope-intercept form to detrmine which has a slope matching the equation in the question.
This equation has the same slope, and is therefore parallel.
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Which of these lines is parallel to 
?
Which of these lines is parallel to
Parallel lines have identical slopes with one another. The given line has a slope of 9, so its parallel line must also have a slope of 9. The only other line with a slope of 9 is 
.
Parallel lines have identical slopes with one another. The given line has a slope of 9, so its parallel line must also have a slope of 9. The only other line with a slope of 9 is
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Which of these lines is parallel to 
?
Which of these lines is parallel to
Parallel lines have identical slopes, so you must figure out which of these lines have the same slope as the given line. To determine the slope of the given line, you can rearrange it to resemble the 
form. 
can be rearranged to 
. Looking at the rearranged equation, it is clear that the line's slope is 
. The only other line with a slope of 
is 
.
Parallel lines have identical slopes, so you must figure out which of these lines have the same slope as the given line. To determine the slope of the given line, you can rearrange it to resemble the
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Which of these lines is parallel to 
Which of these lines is parallel to
Parallel lines have identical slopes. Since all of these lines are in the 
form, you can easily determine their slopes (
). The slope of the given line is 
, so a line that's parallel to it must have the same slope. The only other line with a slope of 
is 
.
Parallel lines have identical slopes. Since all of these lines are in the
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Which of the following lines is parallel to 
?
Which of the following lines is parallel to
Two lines can only be parallel if they have identical slopes. In this case, the slope is 
, which is equal to 
. The only line that has the same slope is
so that is the correct answer. Take note that the 
value does not matter when determining whether two lines are parallel, unless the values are the same, in which case the lines would be identical and not parallel.
Two lines can only be parallel if they have identical slopes. In this case, the slope is
so that is the correct answer. Take note that the
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What is the relationship of the lines depicted by the following equations?
What is the relationship of the lines depicted by the following equations?
The first equation is written in standard form: 
. In this format, the slope is equal to 
.
The second equation is written in slope-intercept form: 
. The slope is given by the value of 
.
Because the slopes of both lines are equal, the lines must be parallel.
The first equation is written in standard form:
The second equation is written in slope-intercept form:
Because the slopes of both lines are equal, the lines must be parallel.
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Two lines are parallel to each other. One of the lines has an equation of 
. What could be the equation of the other line?
Two lines are parallel to each other. One of the lines has an equation of
Parallel lines have identical slopes to one another. The slope of the given line is 7, so the slope of the other line must also be 7. The only other equation with a slope of 7 is 
.
Parallel lines have identical slopes to one another. The slope of the given line is 7, so the slope of the other line must also be 7. The only other equation with a slope of 7 is
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Which of the following pairs of lines are parallel?
Which of the following pairs of lines are parallel?
Lines can be written in the slope-intercept form:
In this form, 
equals the slope and 
represents where the line intersects the y-axis.
Parallel lines have the same slope: 
.
Only one choice contains tow lines with the same slope.
The slope for both lines in this pair is 
.
Lines can be written in the slope-intercept form:
In this form,
Parallel lines have the same slope:
Only one choice contains tow lines with the same slope.
The slope for both lines in this pair is
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Which of the following lines is parallel to 
?
Which of the following lines is parallel to
For two lines to be parallel, they must have the same slope. So, we are looking for a line with a slope of 
. However, it's difficult to tell what the slopes of the answer choices are because they are not in slope-intercept form. Luckily, it's easy to convert them.
Take the answer choice 
. Subtracting 
from both sides gives
which can be simplified to
This is our answer! To be safe, the other choices can be rewritten in slope-intercept form as well, upon which it becomes clear that none of them are parallel.
For two lines to be parallel, they must have the same slope. So, we are looking for a line with a slope of
Take the answer choice
which can be simplified to
This is our answer! To be safe, the other choices can be rewritten in slope-intercept form as well, upon which it becomes clear that none of them are parallel.
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Which of these lines is parallel to
Which of these lines is parallel to
Parallel lines have identical slopes. The slope of the given line is 8, so the slope of the parallel line must also be 8. The only other line with a slope of 8 is
.
Parallel lines have identical slopes. The slope of the given line is 8, so the slope of the parallel line must also be 8. The only other line with a slope of 8 is
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Determine if the lines are parallel perpendicular or neither.
and 
Determine if the lines are parallel perpendicular or neither.
To find out if lines are parallel or perpendicular you must look at the slopes of both lines. If they have the same slope then they are parallel and go in the same direction. If they have opposite slopes, then they are perpendicular and go in opposite directions and will eventually cross eachother at a right angle.
We have the following equations:
and 
They are written in slope-intercept form:
In this form, 
is the slope. The slopes are both 
in our equations; therefore, the lines are parallel.
To find out if lines are parallel or perpendicular you must look at the slopes of both lines. If they have the same slope then they are parallel and go in the same direction. If they have opposite slopes, then they are perpendicular and go in opposite directions and will eventually cross eachother at a right angle.
We have the following equations:
They are written in slope-intercept form:
In this form,
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Find a line parallel to
.
Find a line parallel to
For lines to be parallel, they need to have the same slope. In the form 
we know 
is the slope of the function. Therefore, has 
.
Now looking at the possible answer choices we see that,
can be written in slope-intercept form by dividing both sides by two, which equals
.
We can see that this equation also has slope 
, the same as the given equation. Thus these two lines are parallel.
For lines to be parallel, they need to have the same slope. In the form
Now looking at the possible answer choices we see that,
can be written in slope-intercept form by dividing both sides by two, which equals
We can see that this equation also has slope
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