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To find the linear equation that gives the rule for the table, we need to calculate the slope and then determine the y-intercept.

The table provided shows:

| x  | y  |
|----|----|
| 3  | 58 |
| 4  | 65 |
| 5  | 72 |
| 6  | 79 |

### Step 1: Find the Slope (m)
The slope \( m \) of a line is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points (3, 58) and (4, 65):

\[
m = \frac{65 - 58}{4 - 3} = \frac{7}{1} = 7
\]

The slope is \( m = 7 \).

### Step 2: Find the Y-intercept (b)
The slope-intercept form of a linear equation is:

\[
y = mx + b
\]

Now, using the point (3, 58) and the slope \( m = 7 \), we substitute into the equation to find \( b \):

\[
58 = 7(3) + b
\]
\[
58 = 21 + b
\]
\[
b = 58 - 21 = 37
\]

### Final Equation:
Thus, the equation of the line is:

\[
y = 7x + 37
\]

You can enter this equation as the answer.

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you find the slope between two points?
2. What are the steps to derive the slope-intercept form of a line?
3. Can you explain how to verify a point fits into an equation?
4. What does the slope represent in a real-world context?
5. How do we interpret the y-intercept in this situation?

**Tip:** Always recheck the calculation by plugging a few points from the table into the equation to make sure it holds true.

Write the linear equation that gives the rule for this table.
| x  | y  |
|----|----|
| 3  | 58 |
| 4  | 65 |
| 5  | 72 |
| 6  | 79 |
Write your answer as an equation with y first, followed by an equals sign.

Learn how to derive a linear equation from a table of values using the slope-intercept form. This example uses the points (3, 58), (4, 65), (5, 72), and (6, 79) to find the equation y = 7x + 37. Suitable for students in Grades 7-9.

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