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.