General Form of Equation of A Line

Discussion in 'Algebra' started by nycmathguy, Jun 27, 2021.

  1. nycmathguy

    nycmathguy

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    See attachment for question. I need help questions 82 and 86.

    20210627_155651.jpg
     
    nycmathguy, Jun 27, 2021
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  2. nycmathguy

    MathLover1

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    81.

    x/a+y/b=1

    x-intercept: (a,0)=(3,0)
    y-intercept: (0,b)=(0,5)

    x/3+y/5=1

    (x/3)*15+(y/5)15=1*15

    5x+3y=15


    82.

    x-intercept: (a,0)=(-3,0)
    y-intercept: (0,b)=(0,4)

    x/-3+y/4=1

    (-x/3)*12+(y/4)12=1*12

    -4x+3y=12

    83.

    x-intercept: (a,0)=(-1/6,0)
    y-intercept: (0,b)=(0,-2/3)

    x/(-1/6)+y/(-2/3)=1
    6x/(-1)+3y/(-2)=1 ......multiply by 2
    -12x+3y=2

    84.

    x-intercept: (a,0)=(2/2,0)
    y-intercept: (0,b)=(0,-2)

    x/(2/3)+y/(-2)=1
    3x/2+y/(-2)=1 ......multiply by 2
    3x-y=2


    85.
    point on line: (1,2)
    x-intercept: (c,0) =>a=c
    y-intercept: (0,c)=> b=c

    x/a+y/b=1......substitute a and b

    x/c+y/c=1..........use given point (1,2), substitute x and y

    1/c+2/c=1.........solve for c

    3/c=1
    3=c

    x-intercept: (3,0)
    y-intercept: (0,3)

    equation is

    x/3+y/3=1.....multiply by 3
    x+y=3


    86.

    point on line: (-3,4)
    x-intercept: (d,0) =>a=d
    y-intercept: (0,d)=> b=d

    x/a+y/b=1......substitute a and b
    x/d+y/d=1....multiply by d
    x+y=d........use given point (-3,4), substitute x and y
    -3+4=d
    d=1

    x/1+y/1=1
    x+y=1
     
    MathLover1, Jun 27, 2021
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  3. nycmathguy

    MathLover1

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    MathLover1, Jun 27, 2021
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  4. nycmathguy

    nycmathguy

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    Thank you but I only needed 82 and 86 as a guide for me to do the rest.
     
    nycmathguy, Jun 27, 2021
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