Let:
(x1,y1) = (6,7)
m = -1/2
Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-7=-\frac{1}{2}(x-6) \\ y-7=-\frac{1}{2}x+3 \\ y(x)=-\frac{1}{2}x+10 \end{gathered}[/tex]The point S(2,5) lie on the same line if the point satisfies the equation, so:
[tex]\begin{gathered} S(2,5) \\ x=2,y=5 \\ y(2)=5 \\ 5=-\frac{1}{2}(2)+10 \\ 5=-1+10 \\ 5=9 \\ \text{This is false, because} \\ 5\ne9 \end{gathered}[/tex]Since the point doesn't satisfy the equation, we can conclude that the point S(2,5) is not on the same line
