Question

Complete the table
-x + 9y = 9

x 9 18 27 36 45

y

Answer 1

To complete the table for the equation \(-x + 9y = 9\), we'll solve for \(y\) in terms of \(x\).

Starting with the equation:

\[
-x + 9y = 9
\]

Rearranging gives:

\[
9y = x + 9
\]

Now, dividing both sides by 9:

\[
y = \frac{x + 9}{9} = \frac{x}{9} + 1
\]

Now we can calculate \(y\) for each given value of \(x\):

1. For \(x = 9\):
\[
y = \frac{9}{9} + 1 = 1 + 1 = 2
\]

2. For \(x = 18\):
\[
y = \frac{18}{9} + 1 = 2 + 1 = 3
\]

3. For \(x = 27\):
\[
y = \frac{27}{9} + 1 = 3 + 1 = 4
\]

4. For \(x = 36\):
\[
y = \frac{36}{9} + 1 = 4 + 1 = 5
\]

5. For \(x = 45\):
\[
y = \frac{45}{9} + 1 = 5 + 1 = 6
\]

Now, we can fill in the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
9 & 2 \\
18 & 3 \\
27 & 4 \\
36 & 5 \\
45 & 6 \\
\hline
\end{array}
\]

This completes the table with the corresponding values of \(y\) for each \(x\).