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.