Question

Do you think the points $(3,5),(6,8)$ and $(10,12)$ are straight line? Given reasons for your answer.

Answer 1

If the points $(3,5),(6,8)$ and $(10,12)$ lie on a straight line then the slope of line joining the points $(3,5)$ and $(6,8)$ will be equal to the slope of line joining the pounts $(6,8)$ and $(10,12)$.

Therefore,

Slope of line joining the points $(3,5)$ and $(6,8)=\frac{8-5}{6-3}=\frac{3}{3}=1$

Slope of line joining the points $(6,8)$ and $(10,12)=\frac{12-8}{10-6}=\frac{4}{4}=1$

Since two intersecting lines cannot have same slope, thus the given points are straight line.