https://file.aiquickdraw.com/mathbot/file/1727647084468eo7a8zws.jpg

Let's break down the problem based on the image:

### Given:
- $ y $ represents the number of items the public will buy.
- $ x $ represents the price of the item.
- When the price is $4 (i.e., $ x = 4 $), the public buys 610 items (i.e., $ y = 610 $).
- When the price is $18 (i.e., $ x = 18 $), the public buys 540 items (i.e., $ y = 540 $).

### Step 1: Ordered Pairs
We can write these two conditions as ordered pairs:
1. For the lower price of $4: $ (x_1, y_1) = (4, 610) $.
2. For the higher price of $18: $ (x_2, y_2) = (18, 540) $.

### Step 2: Demand Equation in Slope-Intercept Form
We are asked to find the demand equation in the form:
\[
y = mx + b
\]
where $ m $ is the slope and $ b $ is the y-intercept.

#### Finding the slope $ m $:
The formula for slope $ m $ is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the values:
\[
m = \frac{540 - 610}{18 - 4} = \frac{-70}{14} = -5
\]

#### Finding the y-intercept $ b $:
Now, use one of the points, say $ (4, 610) $, and substitute into the equation $ y = mx + b $:
\[
610 = -5(4) + b
\]
\[
610 = -20 + b
\]
\[
b = 630
\]

### Final Demand Equation:
The demand equation is:
\[
y = -5x + 630
\]

Would you like any further clarification or more details? Here are 5 related questions:

1. How would the demand equation change if a different pair of prices were given?
2. What is the significance of the slope in a demand equation?
3. How can you determine the equilibrium price using supply and demand equations?
4. What would happen to the demand if the price increases beyond $18?
5. How can you use this equation to predict demand at a price of $10?

**Tip**: Always check the slope to understand how the demand changes with the price. If the slope is negative, demand decreases as the price increases.

In demand (and supply) problems, y is the number of items the public will buy if the price of the item is x. In particular, if the price is $4 per item, then the public wants to buy 610 items. However, if the price is $18 per item, then the public would want to buy only 540 items. Convert the information into two ordered pairs and find the demand equation in slope-intercept form.

Solve a linear demand problem where y represents the number of items purchased at a given price x. Given two price points ($4 and $18) and corresponding quantities, learn how to find the demand equation in slope-intercept form using algebraic methods. Suitable for high school students.

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