Explanation

Key Concept: If a point lies on a given line (or curve), then the x- and y-coordinates of that point must satisfy the equation of that line (or curve)

So, for each answer choice, we must plug in the x and y values (aka the coordinates) to see whether they satisfy the given equation.

A. \((−5, −13)\)
We get: \(-13= \frac{3(-5)^2+2}{(-5)-1}=\frac{77}{-6}\)
Doesn't work.
ELIMINATE A

B. \((−4, −10)\)
We get: \(-10= \frac{3(-4)^2+2}{(-4)-1}=\frac{50}{-5}=-10\)
WORKS!


C. \((0, 2)\)
We get: \(2= \frac{3(0)^2+2}{(0)-1}=\frac{2}{-1}=-2\)
Doesn't work.
ELIMINATE C


D. \((3, 14 \frac{1}{2})\)
We get: \(14.5= \frac{3(3)^2+2}{3-1}=\frac{29}{2}=14.5\)
WORKS!


E. \((5, 19 \frac{1}{2})\)[/quote]
We get: \(19.5= \frac{3(5)^2+2}{5-1}=\frac{77}{4}=19.25\)
Doesn't work.
ELIMINATE E


Answer: B & D

Cheers,
Bret