Question

Which coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function? A) (5, 12) B) (6, -4) C) (-3, -1) Eliminate D) (-6, -5)

Answer 1

Answer:

D

Step-by-step explanation:

A linear function has an expression $f(x)=ax+b.$ If the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defines  a linear function, then

$\begin{array}{l}4=a\cdot 0+b\\1=a\cdot (-2)+b\\-2=a\cdot (-4)+b\end{array}.$

From the first equation, $b=4.$ Substitute it into the second equation:

$1=-2a+4,\\ \\-2a=-3,\\ \\a=1.5.$

Check it with the third equation:

$1.5\cdot (-4)+4=-6+4=-2.$

Hence the linear function is $f(x)=1.5x+4.$

Now check all options:

A.

$1.5\cdot 5+4=7.5+4=11.5\neq 12.$

B.

$1.5\cdot 6+4=9+4=13\neq -4.$

C.

$1.5\cdot (-3)+4=-4.5+4=-0.5\neq -1.$

D.

$1.5\cdot (-6)+4=-9+4=-5.$