Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Quick question on math?

Write a linear system that has a point of intersection of (2,-4).

(1)

(2)

8 Answers

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  • 2 months ago
    Favourite answer

    Start with slope-intercept form:

    y = mx + b

    Pick an arbitrary value of m:

    m = 1

    y = x + b

    Plug in x=2, y=-4

    -4 = 2 + b

    b = -4 - 2

    b = -6

    There's your first equation:

    y = x - 6

    Now pick a different arbitrary slope:

    m = 2

    y = 2x + b

    Plug in the point again:

    -4 = 2(2) + b

    -4 = 4 + b

    b = -4 - 4

    b = -8

    There's your second equation:

    y = 2x - 8

    You could pick any 2 different values of m and make this work.

    Answer (one of infinitely many possibilities):

    [1] y = x - 6

    [2] y = 2x - 8

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  • 2 months ago

    My solution is

    y=-4

    y=3x-10

  • ?
    Lv 6
    2 months ago

    You can have any slope you want. So pick the slope, and solve for the y-intercept that puts (2, -4) on the line.

    1) Let slope be, say, 6

    y = 6x + b

    -4 = 6(2) + b

    b = -16

    y = 6x - 16 is one line.

    2) Let slope be -3

    y = -3x + b

    -4 = -3(2) + b

    b = 2

    y = -3x + 2 is another line.

  • Anonymous
    2 months ago

    The equation of any straight line through the point (X.Y) is;

    y- Y = m(x-X)

    where m is the gradient.

    X=2 and Y=-4  and you can pick *any* 2 values of m. E.g.

    m=1 gives y-(-4) = 1(x-2 )

    y = x - 6

    m=2 gives  y-(-4) = 2(x-2 )

    y =  2x - 8

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  • 2 months ago

    The simplest way:

    (1) x = 2

    (2) y = -4

  • ?
    Lv 7
    2 months ago

    The equation of a line y₁ passing through (2,-4) with slope 4 is

              y₁ -  -4 = 4(x - 2)

              y₁ = 4x - 12

    The equation of a line y₂ passing through (2, -4) with slope -¾ is

              y₂ -  -4 = -¾(x - 2)          y₂ = -¾x - ⁵⁄₂

    A system of linear equatinons that has a point of intersection of (-2,4) is

              (1) y₁ = 4x - 12   .....................ANS

              (2) y₂ = -¾x - ⁵⁄₂                      .ANS

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  • 2 months ago

    y = -2 x    

    y = x - 6       

  • 2 months ago

    You can set up two general linear equations based on this form:

    y = mx + b

    Where x = 2 and y = -4 in both with different slopes (m).  I'll use m = -1 and m = 2.  That gives us:

    -4 = -1(2) + b and -4 = 2(2) + b

    -4 = -2 + b and -4 = 4 + b

    -2 = b and -8 = b

    Now that we have two b's complete the equations:

    y = -x - 2 and y = 2x - 8

    That is one of many systems of equations that will have the point (2, -4) as a solution.

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