The supply function and the demand function for a product are linear and are determined by the tables that follow.
Supply Function
Price ($)	Quantity
75	125
150	150
300	200
Demand Function
Price ($)	Quantity
75	355
150	330
300	280
(a)
Write an equation for the supply function's price p as a function of q.
p = 
  
Incorrect: Your answer is incorrect.

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.

The supply function and the demand function for a product are linear and are determined by the tables that follow.
Supply Function
Price ($)	Quantity
75	125
150	150
300	200
Demand Function
Price ($)	Quantity
75	355
150	330
300	280
(a)
Write an equation for the supply function's price p as a function of q.
p = 

Learn how to determine the equation for the supply function's price as a function of quantity using linear relationships. This solution covers key algebraic concepts such as slope calculation and the slope-intercept form. Suitable for students in Grades 9-12.

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