Determine the value of K. Points (6, -1) (3, k) (-3, -7) are on the same line.?

x1 = 6

y1 = - 1

x2 = 3

y2 = k

x3 = - 3

y3 = - 7

The slopes between any two points should be equal, so

(y2 - y1) / (x2 - x1) = (y3 - y1) / (x3 - x1) .............. Equation for Slope

[k - (- 1)] / (3 - 6) = [- 7 - (- 1)] / (- 3 - 6)

(k + 1) / - 3 = (- 7 + 1) / - 9

(k + 1) / - 3 = - 6 / - 9

(k + 1) / - 3 = 2/3

k + 1 = - 3(2/3)

k + 1 = - 2

k = - 1 - 2

k = - 3

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The line passes through A(6, - 1), B(3, k) and C(- 3, - 7)

A(6, - 1) and C(- 3, - 7) are the two points on the line

=> Slope of the line = m = {(- 1) - (- 7)}/{6 - (- 3)} = 6/9 = 2/3 -------- (1)

The line contains the points A(6, - 1) and B(3, k)

=> Slope of the line = m = (- 1 - k)/(6 - 3) = - (k + 1)/3 ------ (2)

Equating (1) and (2) we have : - (k + 1)/3 = 2/3

=> - (k + 1) = 2

=> k + 1 = - 2

=> k = - 2 - 1 = - 3

3

Firstly, the slope of the line passing through (6, −1) and (−3, −7) is

∆y/∆x = −6/ − 9 = 2/3

The equation of this line will be y + 1 = 2/3(x − 6) then y = 2/3x − 5,

to find k you find the image of 3 in the last equation to get k = 2/3(3) − 5 = −3.

the slope is 2/3. 3 is 3 left of 6, making K 2 up down from -1. K is -3.