Question

{ (5,4) (3, 6) (2, 7) (8, 1) (x, y)Which could be the fifth ordered pair in the function?A. (5, 7)B. (2, 1)C. (9, 6)

Answer 1

Not A, Not B, Not C,

Step-by-step explanation

Step 1

find the equation of the line,use

P1(5,4) P2(3,6)

a) find the slope

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(6-4)/(3-5)=(2)/(-2)=-1 \\ \end{gathered}`

b) use the slope-y intercep point to find the equation

Let Point= P1

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{replace} \\ y-4=-1(x-5) \\ y-4=-x+5 \\ y=-x+5+4 \\ y=9-x \end{gathered}`

Step 2

to find the fifth ordered pair, replace in the equation and check if it is true.

A(5,7)

then x=5 ,y =7

`\begin{gathered} y=9-x \\ 7=9-5 \\ 7=4,\text{ False} \end{gathered}`

Hence A is a point of the line, it is not the ordered pair

B(2,1)

then

x=2 , y=1

`\begin{gathered} y=9-x \\ 2=9-1 \\ 2=7,\text{ False} \end{gathered}`

Hence B is not a point of the line, it is not the ordered pair

C(9,6)

`\begin{gathered} y=9-x \\ 6=9-9 \\ 6=0,\text{ false} \end{gathered}`

Hence C is not a point of the line, it is not the ordered pair