A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line. The value of x is , and t

Question

A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line.
The value of x is
, and the value of y is
.

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Ariana 2 weeks 2021-10-04T09:19:10+00:00 1 Answer 0

Answers ( )

    0
    2021-10-04T09:20:57+00:00

    The question is incomplete. The complete question is here.

    A line passes through point (-2, 5) and has a slope of 2/3. Points A(x, 3) and B(-2, y) lie on the line.

    The value of x is ___, the value of y is ___.

    Answer:

    The value of x is -5, and the value of y is 5

    Step-by-step explanation:

    The form of a linear equation is y = m x + b, where

    • m is the slope of the line
    • b is the y-intercept (value y at x = 0), to find b substitute x and y in the equation by the coordinates of a point on the line

    ∵ The slope of the line is \frac{2}{3}

    ∴ m = \frac{2}{3}

    ∵ The form of the equation is y = m x + b

    ∴ y =  \frac{2}{3} x + b

    – Substitute x and y by the coordinates of a point on the line

    ∵ The line passes through point (-2 , 5)

    ∴ x = -2 and y = 5

    ∵ 5 =  \frac{2}{3} (-2) + b

    ∴ 5 =  \frac{-4}{3} + b

    – Add \frac{-4}{3} to both sides

    \frac{19}{3} = b

    ∴ y = \frac{2}{3} x + \frac{19}{3}

    ∵ Point A (x , 3) lies on the line

    – Substitute y by 3 to find x

    ∴ 3 = \frac{2}{3} x + \frac{19}{3}

    – Subtract \frac{19}{3} from both sides

    \frac{-10}{3} =  \frac{2}{3} x

    – Divide both sides by  \frac{2}{3}

    ∴ -5 = x

    The value of x = -5

    ∵ Point B (-2 , y) lies on the line

    – Substitute x by -2 to find y

    ∴ y = \frac{2}{3} (-2) + \frac{19}{3}

    ∴ y =  \frac{-4}{3} +  \frac{19}{3}

    ∴ y =  \frac{15}{3}

    ∴ y = 5

    The value of y = 5

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