How to find out if lines are parallel - Algebra 1
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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 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 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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Which of the following are parallel to the line 
?
Which of the following are parallel to the line
Two lines are parallel when they have the same slope. We can determine the slope of a line in the form 
by identifying 
, the coefficient of x.
In this case, a line will be parallel to 
if and only if the coefficient of x is 3.
So we find:
Two lines are parallel when they have the same slope. We can determine the slope of a line in the form
In this case, a line will be parallel to
So we find:
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Suppose 
is an equation modeling the heart rate in beats per minute 
for a test subject given the number of minutes spent exercising 
. Which of these equations represents a person whose heart rate increases at the same rate, but whose total beats per minute will always be less?
Suppose
Parallel lines never cross nor do they diverge. They climb/descend at the same rate. What determines the "steepness" of a line? The slope does. In order for two lines to remain the same distance from each other (to be parallel) for their length , they must have the same rise-over-run (slope).
So for subject A whose HR increases at 
, the steepness of this person's heart rate's increase is the slope 1/5. Any other person whose heart rate increases by the same rate per minute (the slope) will have a HR that never exceeds or diverges (graphically, in the sense of the two lines) from the HR of subject A.
Subject B 
is the only person who HR line increases with same slope and thus remains the same distance from that of Subject A 
.
Parallel lines never cross nor do they diverge. They climb/descend at the same rate. What determines the "steepness" of a line? The slope does. In order for two lines to remain the same distance from each other (to be parallel) for their length , they must have the same rise-over-run (slope).
So for subject A whose HR increases at
Subject B
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Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, 
equals the slope and 
represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
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Find a line parallel to the line with the equation:
Find a line parallel to the line with the equation:
Lines can be written in the slope-intercept format:
In this format, 
equals the line's slope and 
represents where the line intercepts the y-axis.
First, put the given line in 
form.
We need to isolate 
on the left side of the equation. Subtract 
from both sides of the equation.
Simplify.
Divide both sides of the equation by 
.
Simplify. Rember that when a positive number is divided by a negative number, the answer is always negative.
Subtracting a negative number is the same as adding a positive number. Rewrite.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
First, put the given line in
We need to isolate
Simplify.
Divide both sides of the equation by
Simplify. Rember that when a positive number is divided by a negative number, the answer is always negative.
Subtracting a negative number is the same as adding a positive number. Rewrite.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of
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Find a line parallel to the line with the equation:
Find a line parallel to the line with the equation:
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
First, put the given line in form.
We need to isolate on the left side of the equation. Subtract 
from both sides of the equation.
Simplify.
Divide both sides of the eqaution by 
.
Simplify.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
First, put the given line in
We need to isolate
Simplify.
Divide both sides of the eqaution by
Simplify.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of
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Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above
Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above
Find a line parallel to the line with the equation:
Find a line parallel to the line with the equation:
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
First, put the given line in form.
We need to isolate on the left side of the equation. Subtract 
from both sides of the equation.
Simplify.
Divide both sides of the equation by 
. Rember that when a positive number is divided by a negative number, the answer is always negative. Also, when a negative number is divided by a negative number, the answer is always positive.
Simplify.
Subtracting a negative number is the same as adding a positive number. Rewrite.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
First, put the given line in
We need to isolate
Simplify.
Divide both sides of the equation by
Simplify.
Subtracting a negative number is the same as adding a positive number. Rewrite.
Rearrange terms to match the slope-intercept form.
In the given equation:
Parallel lines share the same slope.
Only one of the choices has a slope of
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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 a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above
Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above
Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above
Which of the following lines is parallel to a line with the equation:
Which of the following lines is parallel to a line with the equation:
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation, equals the slope and represents the y-intercept.
The slope of the given line is:
There is only one line with a slope of 
.
For two lines to be parallel, they must have the same slope.
Lines can be written in the slope-intercept form:
In this equation,
The slope of the given line is:
There is only one line with a slope of
Compare your answer with the correct one above