A line is given by the equation 3x + 2y = 4. What is the equation of a line parallel to the given line and passing through the point (6, -3)

Question

A line is given by the equation 3x + 2y = 4. What is the equation of a line parallel to the given line and passing through the point (6, -3)?

Question 13 options:

A. 3x + 2y = 24
B. 3x+ 2y = 12
C. 2x – 3y = 21
D. 2x – 3y = 3

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Adalyn 2 weeks 2021-09-15T01:12:24+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T01:14:23+00:00

    Answer: B. 3x+ 2y = 12

    Step-by-step explanation:

    The equation of a straight line can be represented in the slope intercept form as

    y = mx + c

    Where

    m represents the slope of the line.

    c represents the y intercept

    The equation of the given line is

    3x + 2y = 4

    2y = -3x + 4

    Dividing through by 2, it becomes

    y = – 3x/2 + 2

    Comparing with the slope intercept form, slope = – 3/2

    If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (6, – 3) is – 3/2

    To determine the y intercept, we would substitute m = – 3/2, x = 6 and y = -3 into y = mx + c. It becomes

    – 3 = – 3/2 × 6 + c

    – 3 = – 9 + c

    c = – 3 + 9

    c = 6

    The equation becomes

    y = -3x/2 + 6

    Cross multiplying by 2, it becomes

    2y = – 3x + 12

    3x + 2y = 12

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