Suppose that a market research company finds that at a price of p=$25, they would sell x= 53 tiles each month. If they lower the price to p=$15, then more people will purchase the tile, and they can expect to sell x = 63 tiles month’s time. Find the equation of the line for the demand equation. Write the answer in the form p=mx+b
Solve these two simultaneous equations for m and b:
25 = 53 m + b
15 = 63 m + b
10 = -10 m
m = -1
15 = -63 + b
b = 78
p = -x + 78
To find the equation of the line for the demand equation, we can use the two points provided: (p=$25, x=53) and (p=$15, x=63).
Step 1: Determine the slope (m) of the line.
The slope (m) can be calculated using the formula:
m = (change in y) / (change in x)
Change in x = 63 - 53 = 10
Change in y = 15 - 25 = -10
m = (-10) / (10) = -1
Step 2: Use the slope (m) and one of the given points to find the y-intercept (b).
We can use the first point, (p=$25, x=53), to calculate the y-intercept (b) using the formula:
y = mx + b
53 = (-1) * 25 + b
53 = -25 + b
b = 53 - (-25)
b = 78
Step 3: Write the equation in the form p = mx + b.
In this case, p represents the price of tiles and x represents the quantity demanded.
p = (-1)x + 78
So, the equation for the demand equation is p = -x + 78, or in the form p = mx + b.