Which pair of equations below represent parallel lines? and y = 9 and x = 18 y = 4x + 9 and y = 4x – 9 y = 5x + 15 and y = –5x + 15

Answer:The correct option is 2.Step-by-step explanation:The slope of two parallel lines are equal.The slope intercept form of a line is[tex]y=mx+b[/tex]Where, m is slope and b is y-intercept.In option 1, the equation of lines are[tex]y=9[/tex][tex]x=18[/tex]The first line is a horizontal line and the second line is a vertical line. Therefore they are not parallel line. Option 1 is incorrect.In option 2, the equation of lines are[tex]y=4x+9[/tex][tex]y=4x-9[/tex]By using the slope intercept form of a line, the slope of first line is 4 and the slope of second line is 4.Since the slope of both lines are same, therefore both lines are parallel. Option 2 is correct.In option 2, the equation of lines are[tex]y=5x+15[/tex][tex]y=-5x+15[/tex]By using the slope intercept form of a line, the slope of first line is 5 and the slope of second line is -5.Since the slope of both lines are not same, therefore both lines are not parallel. Option 3 is incorrect.