Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b

Question

Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:

Part A: Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0 (2 points)

Part B: Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0 (2 points)

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Eloise 2 weeks 2022-01-08T16:33:58+00:00 1 Answer 0 views 0

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    2022-01-08T16:35:13+00:00

    Answer:

    Part A) y=\frac{4}{3}x+\frac{14}{3}

    Part B) y=-\frac{3}{4}x+\frac{1}{2}

    Step-by-step explanation:

    Part A) Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0

    we have

    4x-3y-7=0

    Isolate he variable y

    3y=4x-7

    y=\frac{4}{3}x-\frac{7}{3}

    The slope of the given line is

    m=\frac{4}{3}

    Remember that

    If two lines are parallel then their slopes are the same

    therefore

    The slope of the line parallel to the given line is also

    m=\frac{4}{3}

    Find the equation of the line in slope intercept form

    y=mx+b

    we have

    m=\frac{4}{3}

    point\ (-2,2)

    substitute

    2=\frac{4}{3}(-2)+b

    solve for b

    b=2+\frac{8}{3}

    b=\frac{14}{3}

    therefore

    y=\frac{4}{3}x+\frac{14}{3}

    Part B) Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0

    we have

    4x-3y-7=0

    Isolate he variable y

    3y=4x-7

    y=\frac{4}{3}x-\frac{7}{3}

    The slope of the given line is

    m=\frac{4}{3}

    Remember that

    If two lines are perpendicular, then their slopes are opposite reciprocal

    therefore

    The slope of the line perpendicular to the given line is

    m=-\frac{3}{4}

    Find the equation of the line in slope intercept form

    y=mx+b

    we have

    m=-\frac{3}{4}

    point\ (-2,2)

    substitute

    2=-\frac{3}{4}(-2)+b

    solve for b

    b=2-\frac{3}{2}

    b=\frac{1}{2}

    therefore

    y=-\frac{3}{4}x+\frac{1}{2}

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