To find the demand equation, we can assume a linear relationship between the price $p$ and the number of items sold $x$, in the form:

$p = mx + b$

where:

• $x$ is the number of items sold,
• $p$ is the price per item,
• $m$ is the slope of the line (change in price per change in quantity sold),
• $b$ is the y-intercept.

Step 1: Identify the points

From the problem, we have two points:

1. At a price of $90, 110 items are sold: $(x_1, p_1) = (110, 90)$
2. When the price is raised by $60 (making it $150), 40 fewer items are sold (making it 70 items): $(x_2, p_2) = (70, 150)$

Step 2: Calculate the slope $m$

The slope $m$ is given by the formula: $m = \frac{p_2 - p_1}{x_2 - x_1}$

Substitute the values from the two points: $m = \frac{150 - 90}{70 - 110} = \frac{60}{-40} = -1.5$

Step 3: Substitute a point to solve for $b$

Now, use one of the points to solve for $b$. Using $(x_1, p_1) = (110, 90)$:

$p = mx + b$ $90 = (-1.5)(110) + b$ $90 = -165 + b$ $b = 255$

Step 4: Write the demand equation

The demand equation is: $p = -1.5x + 255$

Final Answer:

The demand equation is: $p = -1.5x + 255$

Would you like more details on the steps or have any questions?

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Here are some follow-up questions related to this topic:

1. What is the significance of the slope in the demand equation?
2. How does the demand equation change if the price decreases instead of increases?
3. Can this demand equation help in forecasting future demand if prices are adjusted again?
4. How would you find the quantity sold if a specific price is given?
5. What is the maximum price at which no items will be sold based on this demand equation?

Tip: In a linear demand equation, a negative slope means that as the price increases, the quantity demanded decreases—a fundamental principle in economics.