Ernie calculated the slope between two pairs of points. He found that the slope between (-1, 4) and (0, 0) is -4. He also found that the slo

Question

Ernie calculated the slope between two pairs of points. He found that the slope between (-1, 4) and (0, 0) is -4. He also found that the slope between (2, 7) and (3, 3) is -4. Ernie concluded that all of these points are on the same line. Use the drop-down menus to complete the statements about Ernie’s conclusion.

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Thu Cúc 5 years 2021-07-31T06:06:25+00:00 1 Answers 48 views 0

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  1. huyenthanh
    0
    2021-07-31T06:07:47+00:00
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    Answer:

    Both points do not lie on the same line

    Step-by-step explanation:

    There’s no drop down to select from. However, I’ll answer the question based on whether Ernie’s conclusion is correct or not.

    Given

    Point 1:

    (-1,4) and (0,0)

    Slope: m = -4

    Point 1:

    (2,7) and (3,3)

    Slope: m = -4

    To determine if this conclusion is right or wrong; first, we need to determine the equation of both points using:

    y - y_1 = m(x - x_1)

    For Point 1

    (-1,4) — (x_1,y_1)

    (0,0) — (x_2,y_2)

    Slope: m = -4

    y - y_1 = m(x - x_1) becomes

    y - 4 = -4(x - (-1))

    y - 4 = -4(x +1)

    y - 4 = -4x -4

    Add 4 to both sides

    y - 4 + 4= -4x -4 + 4

    y = -4x

    For Point 2:

    (2,7) — (x_1,y_1)

    (3,3) — (x_2,y_2)

    Slope: m = -4

    y - y_1 = m(x - x_1) becomes

    y -7 = -4(x - 2)

    y -7 = -4x + 8

    Add 7 to both sides

    y -7 +7= -4x + 8 + 7

    y = -4x + 15

    Comparing both equations:

    y = -4x and y = -4x + 15

    Both expressions are not equal.

    Hence, both points do not lie on the same line

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