CPM Homework Help : CC3MN Problem 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.

Hint:

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

More Help 2:

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.

More Help 1:

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.

Answers:

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

Find the rule.
Hint (a):
To find the rule, look for a pattern that can relate the
y-coordinate to the $x$ -coordinate.
More Help (a):
Notice that at $x = 0$ , $y = 2$ .
Also remember that the y-coordinate increases by $2$ for every $3$ units the $x$ -coordinate increases.
Answer (a):
${\it y} = \frac{2}{3}{\it x} + 2$
You can fill in the last y-coordinate in the table by substituting $1$ into the rule.
What is the slope?
Hint (b):
The slope describes how the values increase.
It can be written as:
$\frac{\text{change in }{\it y}}{\text{change in }{\it x}}$
Is this an example of linear or non-linear growth? Justify your answer.
Hint (c):
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