Question

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

Answer 1

5.

Explanation:

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Answer 2

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=- (1)/(7) } \atop {b= (41)/(7) }} \right.`
Knowing, that a=-1/7 and b=41/7, it is possible to write the equation of required line:

`y=- (1)/(7)x+ (41)/(7)`
3. Using coordinates of point B:

`k=- (6)/(7)+ (41)/(7) =5 \ where \ k=y`

Answer: 5.