9. Use Patterns to Write and Solve Equations
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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 |
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 |
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 |