I am so lost, can anyone help me? I don't even understand what the teacher wants out of me with this problem.
Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).
There are to points : (42,20) , (52,10)
m=(20-10)/(42-52)= -1 => m=-1
choose any point from the two points .
(42,20)=(x1,p1)
p-p1=m(x-x1) => p-20=-1(x-42)
p=-x+42+20 => p=-x+62
Of course! I'd be happy to help you understand how to solve this problem.
To find the equation of the line for the demand equation, we can use the formula:
p = mx + b
where p represents the price, x represents the quantity, m represents the slope, and b represents the y-intercept.
In this case, we are given two points: (42, $20) and (52, $10). These points represent the quantity of tiles sold (x) and the corresponding price (p).
We can use these points to calculate the slope (m) of the line using the slope formula:
m = (p2 - p1) / (x2 - x1)
Substituting the values, we have:
m = ($10 - $20) / (52 - 42)
m = (-$10) / 10
m = -$1
Now that we have the slope, we can substitute one of the given points into the equation to solve for the y-intercept (b). Let's use the point (42, $20):
$20 = -$1 * 42 + b
Simplifying, we get:
$20 = -42 + b
b = $20 + 42
b = $62
Therefore, the equation of the line for the demand equation is:
p = -x + $62