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Example Questions
Example Question #21 : Parallel Lines
There are two lines:
2x – 4y = 33
2x + 4y = 33
Are these lines perpendicular, parallel, non-perpendicular intersecting, or the same lines?
None of the other answers
The same
Non-perpendicular intersecting
Perpendicular
Parallel
Non-perpendicular intersecting
To be totally clear, solve both lines in slope-intercept form:
2x – 4y = 33; –4y = 33 – 2x; y = –33/4 + 0.5x
2x + 4y = 33; 4y = 33 – 2x; y = 33/4 – 0.5x
These lines are definitely not the same. Nor are they parallel—their slopes differ. Likewise, they cannot be perpendicular (which would require not only opposite slope signs but also reciprocal slopes); therefore, they are non-perpendicular intersecting.
Example Question #21 : Coordinate Geometry
Which of the above-listed lines are parallel?
and
and
All four lines
None of them
,
, and
,
, and
There are several ways to solve this problem. You could solve all of the equations for . This would give you equations in the form
. All of the lines with the same
value would be parallel. Otherwise, you could figure out the ratio of
to
when both values are on the same side of the equation. This would suffice for determining the relationship between the two. We will take the first path, though, as this is most likely to be familiar to you.
Let's solve each for :
Here, you need to be a bit more manipulative with your equation. Multiply the numerator and denominator of the value by
:
Therefore, ,
, and
all have slopes of
Example Question #1 : How To Find Out If Lines Are Parallel
Which of the following is parallel to the line passing through and
?
Now, notice that the slope of the line that you have been given is . You know this because slope is merely:
However, for your points, there is no rise at all. You do not even need to compute the value. You know it will be . All lines with slope
are of the form
, where
is the value that
has for all
points. Based on our data, this is
, for
is always
—no matter what is the value for
. So, the parallel answer choice is
, as both have slopes of
.
Example Question #4 : How To Find Out If Lines Are Parallel
Which of the following is parallel to ?
The line between the points and
The line between the points and
The line between the points and
The line between the points and
The line between the points and
The line between the points and
To begin, solve your equation for . This will put it into slope-intercept form, which will easily make the slope apparent. (Remember, slope-intercept form is
, where
is the slope.)
Divide both sides by and you get:
Therefore, the slope is . Now, you need to test your points to see which set of points has a slope of
. Remember, for two points
and
, you find the slope by using the equation:
For our question, the pair and
gives us a slope of
:
Example Question #11 : How To Find Out If Lines Are Parallel
Which of the following lines is parallel to:
First write the equation in slope intercept form. Add to both sides to get
. Now divide both sides by
to get
. The slope of this line is
, so any line that also has a slope of
would be parallel to it. The correct answer is
.
Example Question #1 : How To Find Out If Lines Are Parallel
Which pair of linear equations represent parallel lines?
Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation
,
We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.
Example Question #30 : Coordinate Geometry
Which of the following equations represents a line that is parallel to the line represented by the equation ?
Lines are parallel when their slopes are the same.
First, we need to place the given equation in the slope-intercept form.
Because the given line has the slope of , the line parallel to it must also have the same slope.
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