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:

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.