Question

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)

Answer 1

A.

Explanation:

`\text{If set of order pairs belongs to a linear function, then}\\\\(x_1,\ y_1),\ (x_2,\ y_2),\ (x_3,\ y_3)\\\\(y_2-y_1)/(x_2-x_1)=(y_3-y_2)/(x_3-x_2)\\\\=========================`

`A)\\(-5,\ 16),\ (-1,\ 4),\ (3,\ -8),\ (7,\ -20)\\\\(4-16)/(-1-(-5))=(-12)/(4)=-3\\\\(-8-4)/(3-(-1))=(-12)/(4)=-3\\\\(-20-(-8))/(7-3)=(-12)/(4)=-3\\\\\bold{CORRECT}`

`B)\\(5,\ 16),\ (1,\ -4),\ (-3,\ -8),\ (-7,\ -20)\\\\(-4-16)/(1-5)=(-20)/(-4)=5\\\\(-8-(-4))/(-3-1)=(-4)/(-4)=1\\\\\bold{INCORRECT}`

`C)\\(-4,\ 16),\ (-1,\ 4),\ (2,\ -8),\ (6,\ -20)\\\\(4-16)/(-1-(-4))=(-12)/(3)=-4\\\\(-8-4)/(2-(-1))=(-12)/(3)=-4\\\\(-20-(-8))/(6-2)=(-12)/(4)=-3\\\\\bold{INCORRECT}`

`D)\\(5,\ -16),\ (1,\ -4),\ (-3,\ 8),\ (-7,\ -20)\\\\(-4-(-16))/(1-5)=(12)/(-4)=-3\\\\(8-(-4))/(-3-1)=(12)/(-4)=-3\\\\(-20-8)/(-7-(-3))=(-28)/(-4)=7\\\\\bold{INCORRECT}`