Given
A = (3k,8)
B = (k, -3)
Gradient AB = 3
And we have that the gradient of a line joining the two points A and B is:
[tex]\text{Gradiente AB=}\frac{y2-y1}{x2-x1}[/tex]Therefore, we substitute the given values into the gradient equation:
Gradient AB = 3
x1 = 3k
y1 = 8
x2 = k
y2 = -3
[tex]3=\frac{-3-8}{k-3k}[/tex]Then, solve for k.
Simplify:
[tex]3=\frac{-11}{-2k}=\frac{11}{2k}[/tex]Multiply by 2k on both sides:
[tex]\begin{gathered} 2k\cdot3=2k\cdot\frac{11}{2k} \\ 6k=11 \end{gathered}[/tex]Divide by 6 on both sides:
[tex]\begin{gathered} \frac{6k}{6}=\frac{11}{6} \\ k=\frac{11}{6} \end{gathered}[/tex]Answer: k = 11/6
