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To find the equation of the given function, let's look at the pattern of the values in the table:

| \( x \) | \( q(x) \) |
|-------|-----------|
|   0   |    27     |
|   1   |    29     |
|   2   |    31     |
|   3   |    33     |

We can observe that as \( x \) increases by 1, \( q(x) \) increases by 2. This suggests a linear relationship of the form:

\[
q(x) = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

1. **Find the slope \( m \):**

The slope \( m \) is the change in \( q(x) \) divided by the change in \( x \):

\[
m = \frac{\Delta q(x)}{\Delta x} = \frac{29 - 27}{1 - 0} = \frac{2}{1} = 2
\]

2. **Find the y-intercept \( b \):**

Using the point \( (0, 27) \), we can substitute \( m = 2 \) and \( x = 0 \) into the equation \( q(x) = 2x + b \):

\[
27 = 2(0) + b
\]

\[
b = 27
\]

3. **Equation of the function:**

\[
q(x) = 2x + 27
\]

This is the equation that represents the function based on the given table.

Would you like any further details or have any questions?

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Here are 5 related questions to explore further:

1. What would be the value of \( q(4) \) using the derived equation?
2. How would the graph of the function \( q(x) = 2x + 27 \) look like?
3. How do you verify if a function is linear using its table of values?
4. What is the general method to find the equation of a linear function from a set of points?
5. How would the equation change if the values of \( q(x) \) decreased as \( x \) increased?

**Tip:** For any linear function, calculating the slope first is crucial. The slope tells you how much the dependent variable changes for a unit change in the independent variable.

Find the equation of the given function using the table of values where x = {0, 1, 2, 3} and q(x) = {27, 29, 31, 33}.

Learn how to find the equation of a linear function from a table of values where x = {0, 1, 2, 3} and q(x) = {27, 29, 31, 33}. This problem demonstrates the steps to derive the equation q(x) = 2x + 27 using basic algebraic techniques. Suitable for students in Grades 7-9.

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