Suppose a market research company finds that at a price (y) of $30, they would sell x =10 t-shirts. If they lower the price to y = $20, then more people would purchase the t-shirts, and they can expect to sell x = 30 t-shirts.
Find the equation of the line for the demand equation. Hint: Write your final answer in the form y = mx + b.
(x , y)
x = quantity y = price sold
10 30
30 20
(10, 30)
(30, 20)
To get the equation for the line,
1. First calculate M =
2. Use the point slope formula y - y = m(x - x ). Use your slope (m) from step 1 along with one of your points and plug them into the point slope equation. Write your final answer in the form y = mx + b.
To find the equation of the line for the demand equation, follow these steps:
Step 1: Calculate the slope (m).
The slope of a line can be determined using the formula:
m = (change in y) / (change in x)
Let's use the given points (10, 30) and (30, 20) to calculate the slope:
m = (20 - 30) / (30 - 10)
= -10 / 20
= -1/2
So, the slope of the line is -1/2.
Step 2: Use the point-slope formula.
The point-slope formula is given as:
y - y1 = m(x - x1)
Choose one of the given points (x1, y1) to substitute into the formula. Let's use the point (10, 30).
y - 30 = (-1/2)(x - 10)
Now, simplify and rearrange the equation to solve for y, to get the equation in the form y = mx + b:
y - 30 = (-1/2)x + 5
y = (-1/2)x + 35
Therefore, the equation of the line for the demand equation is y = (-1/2)x + 35.