Complete the ordered pairs. Then graph the equation. A) (0, 2), (-2, 0), (3, 5)

Answer 1

A linear equation is the most obvious. If you plot the 3 points they lie on a straight line, y=x+2

5=3+2, 2 =0+2, and 0= -2+2,

other ordered pairs on the line are (1,3) and (-1, 1)

but non-linear equations also could graphically go through those same 3 given points

a cubic equation that satisfies the 3 points is

y= x^3/6 -x^2/6 + 2

5 = (1/6)3^3 - (1/6(3^2) + 2

=27/6 -9/6 +2 = 18/6+2 = 3+2

2 = (1/6)(0^3) - (1/6)0^2+2

= 0 -0 +2

0 = (1/6)(-2)^3 - (1/6)(-2)^2 + 2

= -8/3 + 2/3 +2

= -6/3 +2

=-2 +2

other ordered pairs on the cubic graph include

(1, 2), and (-1, 5/3)

there are an infinite number of ordered pairs that satisfy the linear or the cubic equation.

there are also an infinite number of other non-linear equations that fit those 3 given points, 4th degree and higher equations. quadratic though doesn't fit, at least for parabolas, circles, ellipses, but there could be some hyperbolas through those 3 points.