Question

The set of points (-2, 1), (0, 3), (2, 5) is collinear.

Answer 1

and?

Answer 2

is it true or false?

Answer 3

if you increase the x coordinate, does the y coordinate go up or down in the same ratio for all the points?

Answer 4

Let A(-2,1), B(0,3) and C(2,5).
If the set {A,B,C} is co-linear then :
\[\Large \overrightarrow{AB}=k\overrightarrow{AC}~~~~~~\text {where k is real} \]

Answer 5

So :
\[\Large\begin{pmatrix}0-(-2)\\3-1\end{pmatrix}=k\begin{pmatrix}2-(-2)\\5-1\end{pmatrix}\]
so :
\[\Large \begin{cases}4k=2\\4k=2\end{cases}\]
so :
\[\Large k=2\]
So the set is collinear