Question

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

parallel
perpendicular
skew
intersecting

Answer 1

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.

Answer 2

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.