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Example Questions
Example Question #21 : Coordinate Geometry
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 #22 : Coordinate Geometry
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 #23 : 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.
Example Question #46 : Lines
Line passes through the points
and
. Line
passes through the point
and has a
of
. Are the two lines parallel? If so, what is their slope? If not, what are their slopes?
Yes, the lines are parallel with a slope of .
No, the lines are not parallel. Line has a slope of
and line
has a slope of
.
Yes, the lines are parallel with a slope of .
No, the lines are not parallel. Line has a slope of
and line
has slope
.
Yes, the lines are parallel with a slope of .
Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line contains points
and
, so we can apply our slope formula directly (pay attention to negative signs!)
.
Line contains point
and, since the y-intercept is always on the vertical axis,
. Thus:
The two lines have the same slope, , and are thus identical.
Example Question #47 : Lines
Line is described by the equation
. Line
passes through the points
and
. Are the two lines parallel? If so, what is their slope? If not, what are their slopes?
No, the lines are not parallel. Line has slope
and line
has slope
.
Yes, the lines are parallel, and both lines have slope .
Yes, the lines are parallel, and both lines have slope .
No, the lines are not parallel. Line has slope
and line
has slope
.
No, the lines are not parallel. Line has slope
and line
has slope
.
We are told at the beginning of this problem that line is described by
. Since
is our slope-intecept form, we can see that
for this line. Since parallel lines have equal slopes, we must determine if line
has a slope of
.
Since we know that passes through points
and
, we can apply our slope formula:
Thus, the slope of line is 1. As the two lines do not have equal slopes, the lines are not parallel.
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