### Home > MC2 > Chapter 9 > Lesson 9.1.3 > Problem9-30

9-30.

Complete the table. .

 $x$ $y$ $–6$ $3$ $6$ $0$ $1$ $4$ $2$ $–4$

Notice that there are two known coordinates: $\left(3, 4\right)$ and $\left(0, 2\right)$.

Now notice that for every difference of $3$ in the
$x$-coordinate, the $y$-coordinate changes by $2$.
Use this reasoning to fill in the rest of the table.

The difference in the $y$-coordinate from $x = 0$ to $x = 3$ is $2$. Since $6$ is twice $3$, the difference in the $y$-coordinate from $x = 0$ to $x = 6$ is twice as much.

$\left(−6, −2\right)$ and $\left(−9, −4\right)$

1. Find the rule.

To find the rule, look for a pattern that can relate the y-coordinate to the x-coordinate.

Notice that at $x = 0$, $y = 2$.
Also remember that the y-coordinate increases by $2$ for every $3$ units the $x$-coordinate increases.

${\it y} = \frac{2}{3}{\it x} + 2$
You can fill in the last y-coordinate in the table by substituting $1$ into the rule.

2. What is the slope?

$\frac{\text{Change in }{\it y}}{\text{Change in }{\it x}}$
The slope describes how the values increase.

Complete the table in the eTool below to graph the points.
Click the link at right for the full version of the eTool: MC2 9-30 HW eTool