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Find the equation of the line passing through the points A(4;3) B (-3;-3)

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  • Philip
    Lv 6
    1 month ago

    Line L passes through A(4,3) & B(-3,-3). Slope of a line

    joining 2 points P1(x1,y1) & P2(x2,y2) = (y2-y1)/(x2-x1). 

    Here (x1.y1) = (4,3) & (x2,y2) = (-3,-3). Then slope L =

    (-3-3)/(-3-4) = (6/7). We shall now determine the equation

    of L in slope, y-intercept form. We have y = mx +b as the equation of L where m=slope L and b is the y-intercept of

    L. We have already determined m =(6/7) so y = (6/7)x +b. Now B(-3,-3) is on L. Then -3=(6/7)(-3)+b & b = 3[(6/7)-1] = 3(6-7)/7 = -(3/7). So equation of L is y = (6/7)x - (3/7).

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  • 1 month ago

    The equation of the line passing through the points

    A (4, 3) and B (-3, -3):

    The equation of a line is y = mx where m is the slope. 

    That line passes through the origin. 

    If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m (x - a). 

    That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line.

    y - 3 = m(x - 4)

    y + 3 = m(x + 3)

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  • sepia
    Lv 7
    1 month ago

    The equation of the line passing through the points A(4, 3) and B (-3, -3):

    Line equation

    y=0.8571428571428571x−0.4285714285714288

    Slope

    0.86

    Intercept

    -0.43

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  • 1 month ago

    solve for its slope

    .........y₂ - y₁

     m =-------------

    .........x₂ - x₁

    .........- 3 - 3

    m =------------- = 6/7

    ..........- 3 - 4

    apply slope intercept form 

    y = mx + b

    3 = 6/7(4) + b

    3 = 24/7 + b

    b = 3 - 24/7

    b = -3/7

    The equation of the line is y = 6/7x - 3/7 ...//

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  • TomV
    Lv 7
    1 month ago

    Two point equation of a line:

    y-y₀ = [(y₁-y₀)/(x₁-x₀)](x-x₀)

    Given:

    (x₀, y₀) = (4, 3)

    (x₁, y₁) = (-3, -3)

    Substituting the given points into the formula:

    y-3 = [(-3-3)/(-3-4)](x-4)

    You asked of "the equation", but there are multiple forms of the equation of a line. I'll convert the two point equation into the standard form of the equation. If you want any of the other forms, you can convert the standard form into whatever form you wish.

    y - 3 = (-6/-7)(x-4)

    -7y + 21 = -6x + 24

    Ans:

    Standard form: 6x - 7y = 3

    ==================

    You can verify this equation by substituting the given points into the equation to show they are points on the line.

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