Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Find an equation for the line that passes through the points , (1, -2 ) and , (−5, 6)?

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  • 1 month ago
    Favorite Answer

    Two points form of line

    y – y₁ = (x – x₁)(y₂ – y₁) / (x₂ – x₁)

    y + 2 = (x – 1)(6 + 2) / (–5 – 1)

    y + 2 = (x – 1)(8) / (–6)

    y + 2 = (–4/3)(x – 1)

    3y + 6 = –4x + 4

    3y + 4x + 2 = 0

    or

    3y = – 4x – 2

    y = –(4/3)x – (2/3)

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  • Pope
    Lv 7
    1 month ago

    (6 + 2)(x - 1) - (-5 - 1)(y + 2) = 0

    8x - 8 + 6y + 12 = 0

    8x + 6y + 4 = 0

    4x + 3y + 2 = 0

    Suit yourself, but I prefer general form. Notice that it involves no division, so there is no risk of division by zero. Also, given integer coordinates, there are no fractional coefficients involved.

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  • 1 month ago

    The equation of the line that passes through the points, (1, -2) and , (−5, 6):

    The Points are (1 , 4)  and  (7, 5) 

    Slope of the line is (6 − -2)/(-5 − 1) = 8/-6 = -4/3

    Equation of line is ( y − 4 ) = 1 6 ( x − 1 ) 6 y −24 = 

    x

    1

    x

    6

    y

    +

    23

    =

    0

    We can use the point-slope formula to write an equation for this line. 

    The point-slope formula states:

    (y − y1) = m(x − x1)

    Where

    m is the slope and  (x1 , y1)  is a point the line passes through. 

    Substituting the slope and values from the point in the problem gives:

    ( y − −2) = 3(x − 1) 

    ( y + 2) = 3(x + 5 ) 

    We can solve for y  if we need to show the equation in slope-intercept form. 

    The slope-intercept form of a linear equation is:

    y = m x + b 

    Where m is the slope and b is the y-intercept value. 

    y + 9 = ( 3 × x ) + ( 3 × 5 ) 

    y + 9 = 3 x + 15 

    y + 9 − 9 = 3 x + 15 − 9 

    y + 0 = 3 x + 6 

    y = 3 x + 6

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  • DWRead
    Lv 7
    1 month ago

                      

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  • m = (6 - (-2)) / (-5 - 1)

    m = (6 + 2) / (-6)

    m = 8/(-6)

    m = -4/3

    y - k = m * (x - h)

    (h , k) is a point on the line

    y - (-2) = (-4/3) * (x - 1)

    y + 2 = (-4/3) * x + (4/3)

    y = (-4/3) * x + (4/3) - 2

    y = (-4/3) * x - (2/3)

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