  ### Home > CC3MN > Chapter 8 > Lesson 8.3.1 > Problem8-127

8-127.

Complete the table.

 $x$ x column 1 $–9$ x column 2 $–6$ x column 3 $0$ x column 4 $1$ x column 5 $3$ x column 6 $6$ $y$ y column 1$–4$ y column 2 is blank. y column 3 $2$ y column 4 is blank. y column 5 $4$ y column 6 is blank.

Notice that there are three known coordinates: $\left(−9, −4\right)$, $\left(0, 2\right)$, and $\left(3, 4\right)$.

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 $\left(6, 6\right)$

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?

The slope describes how the values increase.
It can be written as:

$\frac{\text{change in }{\it y}}{\text{change in }{\it x}}$

3. Is this an example of linear or non-linear growth? Justify your answer.

If you were to graph all of the points in the table, would they form a line?

Complete the table in the eTool below to graph the points.
Click the link at right for the full version of the eTool: 8-127 HW eTool