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

D

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\\eq 12.`

B.

`1.5\cdot 6+4=9+4=13\\eq -4.`

C.

`1.5\cdot (-3)+4=-4.5+4=-0.5\\eq -1.`

D.

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