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The following lines are ______. 4x + 2y = 8 and y = 2x + 4

parallel
perpendicular
skew
intersecting

2 Answers

3 votes

Answer:

Option D.

Explanation:

The slope intercept form of a line is


y=mx+b

where, m is slope and b is y-intercept.

The given lines are


4x+2y=8 ...(i)


y=2x+4 ... (ii)

Rewrite the equation (i) in slope intercept form.


2y=-4x+8

Divide both sides by 2.


y=-2x+4 ...(iii)

On comparing equation (iii) with slope intercept form, we get


m_1=-2

On comparing equation (ii) with slope intercept form, we get


m_2=2

Since
m_1\\eq m_2, therefore lines are not parallel.

Since
m_1\cdot m_2\\eq -1, therefore lines are not perpendicular.

Both lines lies on same plane, i.e., xy-plane, so they are not skew line.

Since both lines lie on same plane and they neither parallel nor perpendicular, therefore they intersecting lines.

Hence, option D is correct.

User Kapilfreeman
by
7.6k points
4 votes
When we want to determine the relative position of two lines, the first thing we can do is to write them in the same form.

We can use the form y=mx+k, where m is the slope.

the given lines are lines in plane. The "skew" case cannot be considered.

i) if 2 lines have same slope, but different k, then they are parallel,
ii) if 2 lines have equal slope (m) and k, then they are coinciding
iii) if the multiplication of their slopes is -1, then they are perpendicular
iv) if the slopes are not equal, and their multiplication is not -1, then the lines are intersecting

2.
4x+2y=8
2y=-4x+8, divide by 2

y=-2x+4

the other line is y=2x+4

-2 and 2 are not the same so the lines are neither parallel, nor intersecting.

-2 * 2 is not equal to -1, so the lines are neither perpendicular.


The lines are intersecting.



User Bwire
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7.0k points