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Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By=c?

(4,9) and (3,5)

please help

3 Answers

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  • 5 years ago

    Let the general equation of a straight line be: y = mx + c ......... (this is the slope-intercept form)

    Since (4, 9) is on the line:

    9 = 4m + c ............................(1)

    And since (3, 5) is also on the line:

    5 = 3m + c ...........................(2)

    Subtracting eqn. (2) from (1), we have:

    9 = 4m + c

    5 = 3m + c

    ---------------------

    4 = m

    Substituting the value of m in eqn. (1) and solving for c:

    9 = 4*4 + c

    c = 9 - 16 = -7

    Substituting the values of m and c in the original equation, we get:

    y = 4x - 7

    y - 4x = -7

    4x - y = 7

    Solution: The equation of the line is 4x - y = 7

    which is in the form: Ax + By = C, where A = 4, B = -1 and C = 7

  • ?
    Lv 7
    5 years ago

    The line through (x₁,y₁) and (x₂,y₂) is given by (x₁-x₂)(y-y₂) = (y₁-y₂)(x-x₂) which can be manipulated to the standard form (y₁-y₂)x - (x₁-x₂)y = y₁x₂ - x₁y₂.

    Here we have (9-5)x - (4-3)y = 9×3 - 4×5, which simplifies to 4x - y = 7

    Graph: https://www.desmos.com/calculator/6vgf0e3ua0

  • David
    Lv 7
    5 years ago

    m = (9 - 5) / (4 - 3)

    m = 4

    y = mx + b

    9 = 4 * 4 + b

    9 = 16 + b

    -7 = b

    y = 4x - 7

    -4x + y = -7

    4x - y = 7

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