Tom's treats can sell 100 candy hearts per week if they are priced at $6 each, and 20 hearts per week if they are priced at $10 each.
What is the linear demand equation (let x=quantity and y=price)?
This means set points (100,6) (20,10) and find m? Then later use the point-slope intercept?
yes,
slope = (10-6)/(20-100) = -1/20
using (20,10)
y-10 = (-1/20)(x-20)
20y - 200 = -x + 20
20y = -x + 220
y = (-1/20)x + 11
And part c says "at what price will there be neither a surplus nor shortage" does that mean equilibrium? And if it is equilibrium would I set both the demand and the supply equations equal to each other?
no, equilibrium means your face, set the demand and supply to your face
watch this video:
www.youtube.com/watch?v=x_pa-FQf_Hw
To find the linear demand equation, we need to determine the slope (m) and the y-intercept (b).
We are given two points on the line: (100, 6) and (20, 10).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points:
m = (10 - 6) / (20 - 100)
m = 4 / -80
m = -1/20
Now that we have the slope (m), we can write the equation of the line as:
y = mx + b
Substituting the values of one of the given points (let's use (100, 6)) and the slope (m) into the equation, we can solve for the y-intercept (b).
6 = (-1/20) * 100 + b
6 = -5 + b
b = 6 + 5
b = 11
Therefore, the linear demand equation is:
y = (-1/20)x + 11
Where x represents the quantity (number of candy hearts) and y represents the price in dollars.