Answer :
Answer:
k = 12
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (8, 20)
m = [tex]\frac{20-4}{8-2}[/tex] = [tex]\frac{16}{6}[/tex] = [tex]\frac{8}{3}[/tex]
Repeat using (5, k) as one of the points and equate to [tex]\frac{8}{3}[/tex]
(x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (5, k) , then
m = [tex]\frac{k-4}{5-2}[/tex] = [tex]\frac{k-4}{3}[/tex] = [tex]\frac{8}{3}[/tex] ( cross- multiply )
3(k - 4) = 24 ( divide both sides by 3 )
k - 4 = 8 ( add 4 to both sides )
k = 12