Question

83. For what value of K will the points (1, 4), (-3, 16) and (k, -2) lie on one straight line.​

Answer 1

k = 3

Explanation:

If the points lie on the same line then the slope between the points will be equal.

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)

m =
`(16-4)/(-3-1)` =
`(12)/(-4)` = - 3

Repeat the process and equate to - 3

with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)

m =
`(-2-4)/(k-1)` =
`(-6)/(k-1)` , then

`(-6)/(k-1)` = - 3 ( multiply both sides by k - 1 )

- 6 = - 3(k - 1) ← divide both sides by - 3

2 = k - 1 ( add 1 to both sides )

3 = k

Answer 2

I don't know

Explanation:

I don't know