Question

Show that the points $A\left(2,5\right),B\left(6,1\right)$and

$C\left(8,-1\right)$lie on a straight line by using slopes.

Short answer

Since all three slopes $m_{1,}{m}_2,m_3$are same so they are lie on a straight line.

Step-by-step solution

Step 1. Given information.

Consider the given information such that the points$A\left(2,5\right),B\left(6,1\right)$and$C\left(8,-1\right)$.

Step 2. Using the slope formula .m=y2-y1x2-x1

Formula used to calculate slope between $A$and $B$,$B$and $C$,$C$and $A$.

$$\begin{gathered} m_{AB}=\frac{1-5}{6-2} \\ {m}_{AB}=-1 \end{gathered}$$

Similarly,$m_{BC}=-1$and$m_{CA}=-1$.