Question

IT ISNT THE 1st OR 2nd HELP LOOK AT IMAGE PLEASE

Answer 1

Last option

Explanation:

First method :

Red Line:

Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).

`slope, m=( 0-7)/(14-0) = -(7)/(14) = -(1)/(2)`

`Equation : (y - 7) = -(1)/(2)(x)`

`2y - 14 = -x\\2y + x = 14\\4y + 2x = 28`
`[ multiply \ by \ 2 \ on \ both \ sides]`

Blue Line:

Take coordinates through which the line passes.

Let it be (-4, -12) and (-10, -9).

`slope, m = (-9 + 14)/(-10) = (5)/(-10) = -(1)/(2)`

`equation : (y + 12) = -(1)/(2) (x+4)\\`

`y = -(1)/(2)x - 2 - 12\\\\y = -(1)/(2)x -14\\\\2y = -x - 28\\\\-2y = x +28`

Second Method:

From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b

And check for set of equation whose slope are same.

First set :

`y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = (9)/(2)x + 5 => slope = (9)/(2)`

Slopes are not equal.

Second set :

`2y = 2x + 5\\y = x + (5)/(2)\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = (3)/(4)x + (5)/(4)\\\\slope = (3)/(4)`

Slopes are not equal.

Third set :

`y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = (2)/(3)x + 2\\\\slope = (2)/(3)`

Slopes are not equal.

Fourth set :

`2x + 4y = 28\\4y = -2x +28\\\\y = -(1)/(2)x + 7\\\\slope = -(1)/(2)\\\\\\-2y = x + 28\\\\y = -(1)/(2)x - 14\\\\slope = -(1)/(2)`

Slopes are same.