Market research has shown that at a price of $230, 100 number of plasma TV’s are sold and if the price is reduced to $190, then 200 number of TV’s are sold. Find the equation that represents this demand curve and state in the form of p=mx+b (Slope Intercept Form of a Linear Equation).
190=200m+b
230=100m+b
subtract the first equation frmo the second.
40=-100m
m= -.4
now, put that m into either equation, and solve for b.
To find the equation that represents the demand curve, we need to determine the slope and y-intercept of the line.
Let's first identify two points on the line: (price, quantity) pairs.
The first point is when the price is $230 and 100 TVs are sold: (230, 100).
The second point is when the price is $190 and 200 TVs are sold: (190, 200).
Next, we will use these two points to find the slope (m) of the line.
The slope (m) is calculated using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Let's substitute the values into the formula:
m = (200 - 100)/(190 - 230)
m = 100/-40
m = -5/2
So, the slope (m) is -5/2.
Now we can find the y-intercept (b) of the line using the slope intercept form of a linear equation: p = mx + b, where p is the price and x is the quantity.
Using one of the points, let's substitute the values of (price, quantity) into the equation to solve for b.
For example, we can use the first point (230, 100):
230 = (-5/2) * 100 + b
230 = -250/2 + b
230 = -125 + b
b = 230 + 125
b = 355
So, the y-intercept (b) is 355.
Putting everything together, the equation representing the demand curve in the form of p = mx + b is:
p = (-5/2)x + 355