Chapter 9.7, Problem 37STP

To determine

The equation corresponding to the given data

Answer to Problem 37STP

Equation B represents the data in the table.

Explanation of Solution

Given:

The given data is:

  

Calculation:

Equation A: $y=2x-4$

Put ‘x’ = -6

  $\begin{array}{l}y=2\left(-6\right)-4\\ y=-12-4\\ y=-16\end{array}$

Equation B: $y=x^2-4$

Put ‘x’ = -6

  $\begin{array}{l}y={\left(-6\right)}^2-4\\ y=36-4\\ y=32\end{array}$

Now put x = -4

  $\begin{array}{l}y={\left(-4\right)}^2-4\\ y=16-4\\ y=12\end{array}$

Now put x = -2

  $\begin{array}{l}y={\left(-2\right)}^2-4\\ y=4-4\\ y=0\end{array}$

Put x = 0

  $\begin{array}{l}y={\left(0\right)}^2-4\\ y=0-4\\ y=-4\end{array}$

Put x = 2

  $\begin{array}{l}y={\left(2\right)}^2-4\\ y=4-4\\ y=0\end{array}$

Since, all the values for ‘x’ correspond to the values of ‘y’ as given in the table, equation B represents the data in the table.

Equation C: $y=4x+8$

Put ‘x’ = -6

  $\begin{array}{l}y=4\left(-6\right)+8\\ y=-24+8\\ y=-16\end{array}$

Equation D: $\begin{array}{l}{x}^2+y=8\\ y=8-x^2\end{array}$

Put ‘x’ = -6

  $\begin{array}{l}y=8-{\left(-6\right)}^2\\ y=8-36\\ y=-28\end{array}$

Equations A, C and D are not describing the data in the given table. Equation B represents the data in the table.