Chapter 8.3, Problem 42STP

To determine

To calculate: To find the equation that represents the table of values for the ordered pair

Answer to Problem 42STP

Equation of line is $3x+y=9$

Explanation of Solution

Given information: Table of ordered pairs

x	-1	0	1	2
y	12	9	6	3

Formula Used:

Equation of line passing through two points is given as

  $y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)$

Calculation:

Table of ordered pairs is given as follows:

x	-1	0	1	2
y	12	9	6	3

Here, line passes though point $\left(0,9\right)$ and $\left(2,3\right)$

Using the two point form, equation of line passing through above points is

  $\begin{array}{l}y-3=\frac{9-3}{0-2}\left(x-2\right)\\ y-3=\frac{6}{-2}\left(x-2\right)\\ y-3=-3\left(x-2\right)\\ y-3=-3x+6\\ y+3x=6+3\\ 3x+y=9\end{array}$

Conclusion:

Hence, equation of line is $3x+y=9$

Correct option is C