Prove the following statement: If the x- and y-intercepts of a line are identical nonzero numbers, the line must have a slope of -1. W

Question

Prove the following statement: If the x- and y-intercepts of a line are identical nonzero numbers, the line must have a slope of -1.
What is the x-intercept you are using?
What is the y-intercept you are using?
Show what you did to prove the slope is -1

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Minh Khuê 4 years 2021-08-22T09:52:00+00:00 1 Answers 80 views 0

Answers ( )

  1. thienthanh
    0
    2021-08-22T09:53:33+00:00
    Reply

    Answer:

    Step-by-step explanation:

    Proof:

    If:

    x intercept is at a number nonzero “a”

    so the point where it intersects the x-axis is at (a,0)

    y-intercept is at the same nonzeronumber “a”

    so the point where it intersects the y-axis is at (0,a)

    Then:

    slope between point (a,0) and (0,a) is m= (y2-y1)/(x2-x1) = 0-a/a-0=-a/a= -1

    x intercept is 2 (for example)

    so the point where it intersects the x-axis is at (2,0)

    y-intercept is 2

    so the point where it intersects the y-axis is at (0,2)

    slope between point (2,0) and (0,2) is m= (y2-y1)/(x2-x1) = 0-2/2-0=-2/2=-1

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