Answer:
D
Step-by-step explanation:
Since the ordered pairs are linear then the slope m between corresponding points will be equal.
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (6, 7) and (x₂, y₂ ) = (2, 5)
m = [tex]\frac{5-7}{2-6}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with (x₁, y₁ ) = (6, 7) and (x₂, y₂ ) = (k, 11)
m = [tex]\frac{11-7}{k-6}[/tex] = [tex]\frac{1}{2}[/tex], that is
[tex]\frac{4}{k-6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
k - 6 = 8 ( add 6 to both sides )
k = 14 → D
