### Home > CC3 > Chapter 9 > Lesson 9.2.1 > Problem9-58

9-58.

Copy and complete the following table.

 $x$ x column 1 $5$ x column 2 is blank. x column 3 $4$ x column 4 is blank. x column 5 $–2$ x column 6 $3$ $y$ y column 1$–17$ y column 2 $–5$ y column 3 is blank. y column 4 $–2$ y column 5 $4$ y column 6 $–11$
1. What is the rule?

Since no $x$-value of $0$ is given, we will have to solve for the rule by finding the slope and then any possible constants.

From Chapter 7, we know that slope is the following:

$\frac{\text{change in }y\text{-values}}{\text{change in }x \text{-values}}$

Choosing any two given set of $x$- and $y$- values, we can find the slope of the equation. For example, choosing $\left(5, −17\right)$ and $(3, −11)$:

$\frac{\text{change in }y\text{-values}}{\text{change in }x \text{-values}} = \frac{-6}{2} = -3$

So far, the rule is $y = −3x$. Test this rule to see if it is complete by substituting in a value of $x$ and checking if the correct $y$-value is given. What do you notice? Is there another constant value that is part of the rule?

$y = −3x − 2$
Use this rule to fill in the table.

2. What is the slope?

What is the slope you solved for the rule in part (a)?

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Click the link at right for the full version of the eTool: 9-58 HW eTool