CPM Homework Help : MC2 Problem 9-30

Complete the table. .

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

Hint:

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

More Help 1:

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 2:

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 $\left(−9, −4\right)$

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):
$\frac{\text{Change in }{\it y}}{\text{Change in }{\it x}}$
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