To find the equation of the supply function, we need to find the linear relationship between price $p$ and quantity $q$.

From the table, the given points for the supply function are:

• $(125, 75)$
• $(150, 150)$
• $(200, 300)$

The general form of a linear equation is: $p = m q + b$ Where:

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

Step 1: Find the slope $m$

The slope $m$ is calculated as: $m = \frac{\Delta p}{\Delta q} = \frac{p_2 - p_1}{q_2 - q_1}$

Using the points $(125, 75)$ and $(200, 300)$: $m = \frac{300 - 75}{200 - 125} = \frac{225}{75} = 3$

Step 2: Find the y-intercept $b$

Now, substitute one of the points (for example, $(125, 75)$) and the slope $m = 3$ into the equation $p = m q + b$: $75 = 3(125) + b$ $75 = 375 + b$ $b = 75 - 375 = -300$

Step 3: Write the equation

Now that we have the slope and y-intercept, the supply function is: $p = 3q - 300$

This is the equation for the supply function.

Would you like more details on this? Here are a few related questions to consider:

1. How do you determine the equation of the demand function?
2. What is the equilibrium point between supply and demand?
3. How do changes in the slope affect the supply curve?
4. Can the supply function have a negative intercept?
5. How does elasticity relate to linear supply functions?

Tip: To verify your function, plug in points from the table and see if they satisfy the equation.