Given the three points to be
[tex](-5,2),\text{ (0, 6), (6,4)}[/tex]
Let A, B, C respectively represent the three points such that
[tex]\begin{gathered} A(-5,2), \\ B(0,\text{ 6),} \\ C(6,\text{ 4)} \end{gathered}[/tex]
The slope m of a line between any two points is given as
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1}\text{ ----- equation 1} \\ \text{where } \\ m\text{ }\Rightarrow slope\text{ of the line} \\ (x_{1,}y_1)\Rightarrow coordinates\text{ of one point} \\ (x_2,y_2)\Rightarrow coordinates\text{ of the other point} \end{gathered}[/tex]
The slope of the line between the second and third points is evaluated as
[tex]\begin{gathered} \text{second point}\Rightarrow B(0,6)\text{ = }(x_1,y_1) \\ \text{third point}\Rightarrow C(6,4)\text{ = }(x_2,y_2) \\ \text{Substitute the above values into equation 1} \\ thus, \\ m\text{ = }\frac{4-6}{6-0}\text{ =}\frac{\text{-2}}{6} \\ \Rightarrow m=-\frac{1}{3} \\ \\ \end{gathered}[/tex]
Hence, the slope between the second and third points is evaluated to be
[tex]-\frac{1}{3}[/tex]
