Q:

Which set of ordered pairs belongs to a linear function?A) (-5, 16).(-1,4),(3, - 8), (7, -20)B) (5, 16), (1, -4),(-3, -8).(-7, -20)C) (-4,16).(-1,4), (2, - 8), (6, -20)D) (5, -16), (1, - 4),(-3, 8), (-7,-20)

Accepted Solution

A:
Answer:A.Step-by-step explanation:[tex]\text{If set of order pairs belongs to a linear function, then}\\\\(x_1,\ y_1),\ (x_2,\ y_2),\ (x_3,\ y_3)\\\\\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_3-y_2}{x_3-x_2}\\\\=========================[/tex][tex]A)\\(-5,\ 16),\ (-1,\ 4),\ (3,\ -8),\ (7,\ -20)\\\\\dfrac{4-16}{-1-(-5)}=\dfrac{-12}{4}=-3\\\\\dfrac{-8-4}{3-(-1)}=\dfrac{-12}{4}=-3\\\\\dfrac{-20-(-8)}{7-3}=\dfrac{-12}{4}=-3\\\\\bold{CORRECT}[/tex][tex]B)\\(5,\ 16),\ (1,\ -4),\ (-3,\ -8),\ (-7,\ -20)\\\\\dfrac{-4-16}{1-5}=\dfrac{-20}{-4}=5\\\\\dfrac{-8-(-4)}{-3-1}=\dfrac{-4}{-4}=1\\\\\bold{INCORRECT}[/tex][tex]C)\\(-4,\ 16),\ (-1,\ 4),\ (2,\ -8),\ (6,\ -20)\\\\\dfrac{4-16}{-1-(-4)}=\dfrac{-12}{3}=-4\\\\\dfrac{-8-4}{2-(-1)}=\dfrac{-12}{3}=-4\\\\\dfrac{-20-(-8)}{6-2}=\dfrac{-12}{4}=-3\\\\\bold{INCORRECT}[/tex][tex]D)\\(5,\ -16),\ (1,\ -4),\ (-3,\ 8),\ (-7,\ -20)\\\\\dfrac{-4-(-16)}{1-5}=\dfrac{12}{-4}=-3\\\\\dfrac{8-(-4)}{-3-1}=\dfrac{12}{-4}=-3\\\\\dfrac{-20-8}{-7-(-3)}=\dfrac{-28}{-4}=7\\\\\bold{INCORRECT}[/tex]