Question

A line contains the points (-1, 6), (6, k) and (20, 3). What is the value of k?

Answer 1

Consider, pls, this option:
1. if a required line has a form y=ax+b, then points A(-1;6); B(6;k) and C(20;3) belong to it.
2. According to the item 1 it is possible to make up the system of equations for A and C:
$\left \{ {{-a+b=6} \atop {20a+b=3}} \right \ \left \{ {{a=- \frac{1}{7} } \atop {b= \frac{41}{7} }} \right.$
Knowing, that a=-1/7 and b=41/7, it is possible to write the equation of required line:
$y=- \frac{1}{7}x+ \frac{41}{7}$
3. Using coordinates of point B:
$k=- \frac{6}{7}+ \frac{41}{7} =5 \ where \ k=y$

Answer: 5.