Answer:
Last option
Step-by-step explanation:
First method :
Red Line:
Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).
[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]
[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]
[tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex] [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]
Blue Line:
Take coordinates through which the line passes.
Let it be (-4, -12) and (-10, -9).
[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]
[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]
[tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]
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 :
[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]
Slopes are not equal.
Second set :
[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]
Slopes are not equal.
Third set :
[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]
Slopes are not equal.
Fourth set :
[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]
Slopes are same.
