Find the supply equation using the given information. (Let x be the number of items.)
At a price of $1500 a supplier will supply 170 items. If the price decreases by $100, then the supplier will supply 20 fewer items.

To find the supply equation, we can assume it is a linear equation of the form:

\[
p = mx + b
\]

Where:
- $ p $ is the price per item,
- $ x $ is the number of items supplied,
- $ m $ is the slope of the line (which represents the rate at which the price changes with respect to the number of items), and
- $ b $ is the y-intercept (which represents the price when the number of items supplied is zero).

### Step 1: Determine the slope ($ m $)
The slope $ m $ can be calculated using the change in price and the change in the number of items supplied:

\[
m = \frac{\text{Change in price}}{\text{Change in quantity}} = \frac{\Delta p}{\Delta x}
\]

Given:
- When $ x = 170 $, $ p = 1500 $
- When $ x = 170 - 20 = 150 $, $ p = 1500 - 100 = 1400 $

Thus:

\[
m = \frac{1400 - 1500}{150 - 170} = \frac{-100}{-20} = 5
\]

### Step 2: Find the y-intercept ($ b $)
Using the slope and one of the points, we can find $ b $:

Using the point $ (x, p) = (170, 1500) $:

\[
1500 = 5(170) + b
\]

\[
1500 = 850 + b
\]

\[
b = 1500 - 850 = 650
\]

### Step 3: Write the supply equation
Now, we can write the supply equation using the values of $ m $ and $ b $:

\[
p = 5x + 650
\]

So, the supply equation is:

\[
\boxed{p = 5x + 650}
\]

This equation indicates that for each additional item supplied, the price increases by $5, starting from a base price of $650.

Would you like more details or have any questions?

Here are some related questions you might consider:
1. How would the supply equation change if the price decrease was $200 instead of $100?
2. What is the quantity supplied when the price is $2000?
3. How can you graph the supply equation, and what does the graph represent?
4. If the price drops to $1000, how many items will the supplier provide?
5. What would be the impact on the supply equation if the supplier's costs increased, requiring a higher base price?

**Tip:** In linear supply and demand problems, understanding the slope can help predict how changes in price affect quantity and vice versa.

Find the supply equation using the given information. (Let x be the number of items.) At a price of $1500 a supplier will supply 170 items. If the price decreases by $100, then the supplier will supply 20 fewer items.

Learn how to find the supply equation using the linear relationship between price and quantity. This problem demonstrates the use of the slope-intercept formula to determine the rate of change in price based on supply and demand, suitable for Grades 9-12.

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