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 =

Question

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

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Answers ( No )

    0
    2021-10-14T23:10:51+00:00

    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

    y=mx+b

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

    In option 1, the equation of lines are

    y=9

    x=18

    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

    y=4x+9

    y=4x-9

    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

    y=5x+15

    y=-5x+15

    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.

    0
    2021-10-14T23:10:59+00:00

    Answer:

    Option B.

    Step-by-step explanation:

    If two lines are in the form of y = mx + c and y’ = m’x’ + c’

    and the given lines are parallel then their slopes will be same.

    For this condition m = m’

    Now we will analyse each option for the condition that the given lines are parallel lines.

    Option A. y = 9 and x = 18

    These lines are horizontal and vertical lines so they are not parallel.

    Option B. y = 4x + 9 and y = 4x – 9

    y = 4x + 9 slope of the line is m = 4

    y = 4x – 9 slope of this line is m’ = 4

    Slopes are same so both the lines are parallel.

    Option C. y = 5x + 15 and y = -5x + 15

    for y = 5x + 15 slope m = 5

    for y = -5x + 15 slope m’ = -5

    Slopes are not equal so the lines are not parallel.

    Option B. is the answer.

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