Question

Ernie calculated the slope between two pairs of points. He found that the slope between ( ( -1, 4) 1 , 4 ) and (0, 0) ( 0 , 0 ) is -4 4 . He also found that the slope between (2, 7) ( 2 , 7 ) and (3, 3) ( 3 , 3 ) is -4 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.

Answer 1

Okay so this picture is basically the answer for anyone who needs it...

Explanation:

Answer 2

His conclusion was incorrect.

Explanation:

Since, slope of a line passes through
`(x_1, y_1)` and
`(x_2, y_2)` is,

`m=(y_2-y_1)/(x_2-x_1)`

Thus, the slope between (-1, 4) and (0, 0),

`m_1=(0-4)/(0+1)=-4`

Also, the slope between (2, 7) and (3, 3),

`m_2=(3-7)/(3-2)=(-4)/(1)=-4`

Now,

There are two cases possible,

Case 1 : line passes through (-1, 4) and (0, 0) is parallel to line passes through (2, 7) and (3, 3)

Case 2 : (-1, 4), (0, 0), (2, 7) and (3, 3) are on the same line

Hence, we can not say that they are on same line only after getting same slope.

i.e. his conclusion was incorrect.