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

Answer:

His conclusion was incorrect.

Step-by-step explanation:

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

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m_1=\frac{0-4}{0+1}=-4$

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

$m_2=\frac{3-7}{3-2}=\frac{-4}{1}=-4$

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.