Complete the point-slope equation of the line through (2,3 and (7,4). Use exact numbers.

Question

Complete the point-slope equation of the line through (2,3 and (7,4). Use exact numbers.

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Aubrey 3 weeks 2021-09-24T05:13:17+00:00 1 Answer 0

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    2021-09-24T05:15:16+00:00

    The point-slope equation of the line is y-3=\frac{1}{5}(x-2)

    Step-by-step explanation:

    The form of the point-slope equation is y-y_{1}=m(x-x_{1}) , where

    • m is the lope of the line
    • (x_{1},y_{1}) is a point lies on the line

    The slope of a line m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , where

    (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line

    ∵ The line through (2 , 3) and (7 , 4)

    x_{1} = 2 and x_{2} = 7

    y_{1} = 3 and y_{2} = 4

    – Substitute these value in the rule of the slope

    m=\frac{4-3}{7-2}=\frac{1}{5}

    ∴ the slope of the line is m=\frac{1}{5}

    Let us substitute the value of the slope and the coordinates of point (x_{1},y_{1}) in the form of the equation

    y-y_{1}=m(x-x_{1})

    x_{1} = 2 and y_{1} = 3

    m=\frac{1}{5}

    y-3=\frac{1}{5}(x-2)

    The point-slope equation of the line is y-3=\frac{1}{5}(x-2)

    Learn more:

    You can learn more about the linear equation in brainly.com/question/12941985

    #LearnwithBrainly

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