Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).

Question

Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).

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Charlie 2 weeks 2021-09-13T11:42:51+00:00 1 Answer 0

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    2021-09-13T11:44:33+00:00

    Answer:

    5x – 2y = -4

    Step-by-step explanation:

    The point-slope form of an equation of a line:

    y-y_1=m(x-x_1)

    m – slope

    Te formula of a slope:

    m=\dfrac{y_2-y_1}{x_2-x_1}

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

    We have two points: (2, -3) and (4, 2). Substitute:

    m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}

    y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)

    Convert it to the standard form Ax+By=C:

    y+3=\dfrac{5}{2}(x-2)           multiply both sides by 2

    2y+6=5(x+2)        use the coordinates of the point

    2y+6=5x+10          subtract 6 from both sides

    2y=5x+4              subtract 5x from both sides

    -5x+2y=4        change the signs

    5x-2y=-4

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