How to find the equation of a parallel line - PSAT Math
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Which of the following is the equation of a line that is parallel to the line 4_x_ – y = 22 and passes through the origin?
Which of the following is the equation of a line that is parallel to the line 4_x_ – y = 22 and passes through the origin?
We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4_x_ – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.
In 4_x_ – y = 0 we can rearrange to get y = 4_x_. This fulfills both requirements.
We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4_x_ – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.
In 4_x_ – y = 0 we can rearrange to get y = 4_x_. This fulfills both requirements.
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What line is parallel to 2x + 5y = 6 through (5, 3)?
What line is parallel to 2x + 5y = 6 through (5, 3)?
The given equation is in standard form and needs to be converted to slope-intercept form which gives y = –2/5x + 6/5. The parallel line will have a slope of –2/5 (the same slope as the old line). The slope and the given point are substituted back into the slope-intercept form to yield y = –2/5x +5.
The given equation is in standard form and needs to be converted to slope-intercept form which gives y = –2/5x + 6/5. The parallel line will have a slope of –2/5 (the same slope as the old line). The slope and the given point are substituted back into the slope-intercept form to yield y = –2/5x +5.
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What line is parallel to 
through 
?
What line is parallel to
The slope of the given line is 
and a parallel line would have the same slope, so we need to find a line through 
with a slope of 2 by using the slope-intercept form of the equation for a line. The resulting line is 
which needs to be converted to the standard form to get 
.
The slope of the given line is
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In the 
-plane, the line 
is parallel to the line 
. What is the value of 
?
In the
In this equation, 
is equal to the slope of the line. You have been given a line parallel to the line containing variable 
, and since parallel lines have the same slope, all you need to do is figure out the slope of 
in order to figure out what 
is. To figure out the slope of 
, you need to convert the equation into 
form, which means isolating 
on one side of the equation.
Given this solution, the slope of the parallel lines, and thus 
, is equal to 2.
In this equation,
Given this solution, the slope of the parallel lines, and thus
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Find the equation of a line parallel to 
that also passes through the point 
.
Find the equation of a line parallel to
Since they are parallel, the line will have the same slope as 
.
Thus, it will take the form 
.
We then use the point (3,2) to solve for 
:
so the equation of the line is
Since they are parallel, the line will have the same slope as
Thus, it will take the form
We then use the point (3,2) to solve for
so the equation of the line is
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Which of the following lines has zero points of intersection with the line, 
?
Which of the following lines has zero points of intersection with the line,
This prompt asks you to find a line that is parallel to the one given. Parallel lines have no points of intersection (as opposed to intersecting lines which have 1 point of intersection). Parallel lines have the same slope, but different y-intercepts. If they had the same y-intercept, then they would actually be the same line.
We can find the slope of the first line by converting it to slope-intercept form.
First, subtract 3x from both sides.
Then, divide both sides by -2.
The slope of the line is 3/2. The only answer that has that same slope, but a different y-intercept is 
.
This prompt asks you to find a line that is parallel to the one given. Parallel lines have no points of intersection (as opposed to intersecting lines which have 1 point of intersection). Parallel lines have the same slope, but different y-intercepts. If they had the same y-intercept, then they would actually be the same line.
We can find the slope of the first line by converting it to slope-intercept form.
First, subtract 3x from both sides.
Then, divide both sides by -2.
The slope of the line is 3/2. The only answer that has that same slope, but a different y-intercept is
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