Respuesta :
Answer:
k = 3
Step-by-step 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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)
m = [tex]\frac{16-4}{-3-1}[/tex] = [tex]\frac{12}{-4}[/tex] = - 3
Repeat the process and equate to - 3
with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)
m = [tex]\frac{-2-4}{k-1}[/tex] = [tex]\frac{-6}{k-1}[/tex] , then
[tex]\frac{-6}{k-1}[/tex] = - 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
