Envision Math 2.0: Grade 6, Volume 1
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9. Use Patterns to Write and Solve Equations
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Exercise 11 Page 237

How does the dependent variable y change, when the independent variable x changes?

Rule: The value of y is equal to the value of x divided by 9.
Equation: y=x Ă· 9
Table:

x 0 9 18 27 36
y 0 1 2 3 4
Practice makes perfect

Let's find the pattern that describes the relation between the dependent variable y and the independent variable x. Note that if we divide the value of x by 9 we get the value of y. We can include this information in the given table.

x 0 9 18 27 36
Pattern 0 Ă· 9 9 Ă· 9 18 Ă· 9
y 0 1 2
Now we want to write an equation to describe this relationship.

the value ofxdivided by 9=the value ofy x ÷ 9=y y=x ÷ 9 We can use this equation to calculate the missing values. Let's decide the value for y when x is 27 and 36. y= 27÷ 9 → y= 3 y= 36÷ 9 → y= 4 Finally, we complete the table.

x 0 9 18 27 36
Pattern 0 Ă· 9 9 Ă· 9 18 Ă· 9 27 Ă· 9 36 Ă· 9
y 0 1 2 3 4