Chapter 1.5, Problem 12PPS

To determine

To find: The equation that represents the relationship between the $xandy$ values.

Answer to Problem 12PPS

Option $C$ $y=-3x+1$ is the correct answer.

Explanation of Solution

Given information: A table containing relevant data values and four choices.

Calculation:

Putting $(-2,7)$ in option $Ay=x+9$ ,

  $\begin{array}{l}7=-2+9\\ 7=7,\text{which}\text{is}\text{true}\end{array}$

Putting $(2,-5)$ in option $Ay=x+9$ ,

  $\begin{array}{l}-5=2+9\\ -5=11,\text{which}\text{is}\text{false}\end{array}$

Option $A$ is not the answer,

Putting $(-2,7)$ in option $By=x^2+3$ ,

  $\begin{array}{l}$ 7={(-2)}^2+3$7=4+3\\ 7=7,\text{which}\text{is}\text{true}\end{array}$

Putting $(2,-5)$ in option $By=x^2+3$ ,

  $\begin{array}{l}$ 5={(2)}^2+3$-5=7,\text{which}\text{is}\text{false}\end{array}$

Option $B$ is not the answer,

Similarly calculating the values for option $Cy=-3x+1$ and arranging them in table,

  $\begin{array}{llllll}x\hfill & -2\hfill & 2\hfill & 4\hfill & 6\hfill & 10\hfill \\ y\hfill & 7\hfill & -5\hfill & -11\hfill & -17\hfill & -29\hfill \end{array}$

The above table matches the given table.

Thus, option $C$ $y=-3x+1$ is the correct answer.