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)
Accepted Solution
A:
Answer:DStep-by-step explanation:A linear function has an expression [tex]f(x)=ax+b.[/tex] If the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defines a linear function, then[tex]\begin{array}{l}4=a\cdot 0+b\\1=a\cdot (-2)+b\\-2=a\cdot (-4)+b\end{array}.[/tex]From the first equation, [tex]b=4.[/tex] Substitute it into the second equation:[tex]1=-2a+4,\\ \\-2a=-3,\\ \\a=1.5.[/tex]Check it with the third equation:[tex]1.5\cdot (-4)+4=-6+4=-2.[/tex]Hence the linear function is [tex]f(x)=1.5x+4.[/tex]Now check all options:A.[tex]1.5\cdot 5+4=7.5+4=11.5\neq 12.[/tex]B. [tex]1.5\cdot 6+4=9+4=13\neq -4.[/tex]C. [tex]1.5\cdot (-3)+4=-4.5+4=-0.5\neq -1.[/tex]D. [tex]1.5\cdot (-6)+4=-9+4=-5.[/tex]