To solve this problem, we are looking for the equation of a line in the form:

$y = mx + b$

where:

• $m$ is the slope, and
• $b$ is the y-intercept.

Step 1: Calculate the slope $m$

The slope $m$ is calculated using the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Using two points from the table, for example, $(2, 184)$ and $(3, 317)$:

$m = \frac{317 - 184}{3 - 2} = \frac{133}{1} = 133$

So the slope $m = 133$.

Step 2: Find the y-intercept $b$

Now, we can use the slope and one of the points to find the y-intercept $b$. Using the point $(2, 184)$, substitute into the equation $y = 133x + b$:

$184 = 133(2) + b$ $184 = 266 + b$ $b = 184 - 266 = -82$

Thus, the y-intercept $b = -82$.

Final equation

The linear equation that fits the table is:

$y = 133x - 82$

Would you like further details or have any questions? Here are five related questions you might find interesting:

1. How do you interpret the slope and y-intercept in the context of this problem?
2. Can you use other points from the table to verify the equation?
3. How does changing the slope affect the graph of the line?
4. What happens to the equation if the y-intercept is a positive number?
5. How can you solve for $x$ given a specific $y$ value?

Tip: The slope tells you how much $y$ increases for each unit increase in $x$, while the y-intercept represents the value of $y$ when $x = 0$.