Question

Which two lines are parallel?

5y = 2x-5
5y = 4 +3x
5y-3x = -1
O No two of the lines are parallel.
O I and III
O II and III
O land I

Answer 1

Given:

The equations are

`5y=2x-5`

`5y=4+3x`

`5y-3x=-1`

To find:

The two parallel lines.

Solution:

Slope intercept form of a line is

`y=mx+b`

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

Isolate variable y in each of the given equations, to get the slope intercept form of the lines.

The slope intercept forms of given lines are

`y=(2)/(5)x-1`

`y=(4)/(5)+(3)/(5)x`

`y=-(1)/(5)+(3)/(5)x`

On comparing these equations with slope intercept form, we get

Slope of I line =
`(2)/(5)`

Slope of II line =
`(3)/(5)`

Slope of III line =
`(3)/(5)`

Slope of parallel lines are equal. So, lines II and III are parallel because their slopes are equal.

Therefore, the correct option is C.