Answer:
k = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (6, k)
m = [tex]\frac{k+4}{6-2}[/tex] = [tex]\frac{k+4}{4}[/tex]
Equating the 2 slopes, that is
[tex]\frac{k+4}{4}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
2(k + 4) = 12 ( divide both sides by 2 )
k + 4 = 6 ( subtract 4 from both sides )
k = 2
