for every $1 price increase, sales decrease by 150. So,
Now you can use the point-slope form of the line:
x-375 = -150(p-2.50)
x = 750 - 150p
Find a formula that gives x in terms of p: x=
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell items if the price is $1.50.
Now you can use the point-slope form of the line:
x-375 = -150(p-2.50)
x = 750 - 150p
Let's use the two given data points: (375, $2.50) and (225, $3.50).
First, let's find the slope (m) of the line:
m = (change in y) / (change in x)
= (p - 2.50) / (x - 375)
Using the second data point, (225, $3.50):
3.50 - 2.50 = (p - 2.50) / (225 - 375)
1 = (p - 2.50) / (-150)
Cross multiplying:
-150 = p - 2.50
Now, let's solve for p:
p = -150 + 2.50
p = -147.50
The formula that gives x in terms of p is:
x = (-150(p - 2.50)) / (-150)
Now, we can use this formula to find the number of items sold if the price per item is $1.50.
Let's substitute p = $1.50 into the formula:
x = (-150(1.50 - 2.50)) / (-150)
x = (-150(-1.00)) / (-150)
x = 1
Therefore, if the price per item is $1.50, the company will sell 1 item.
Data point 1: 375 items sold at $2.50 per item
Data point 2: 225 items sold at $3.50 per item
Let's label the number of items sold as x and the price per item as p. We can create two equations using these data points:
Equation 1: x = 375 when p = 2.50
Equation 2: x = 225 when p = 3.50
To find the equation, we need to find the slope (m) and the y-intercept (b) of the line that represents this linear relationship.
First, find the slope:
m = (y2 - y1) / (x2 - x1)
m = (225 - 375) / (3.50 - 2.50)
m = -150 / 1
m = -150
Now, substitute one of the data points and the slope into the slope-intercept form of a linear equation (y = mx + b) to find the y-intercept (b):
375 = -150(2.50) + b
375 = -375 + b
b = 375 + 375
b = 750
Hence, the linear equation that relates the number of items sold (x) to the price per item (p) is:
x = -150p + 750
Now let's use the formula to find the number of items they will sell if the price per item is $1.50. We can substitute p = 1.50 into the equation:
x = -150(1.50) + 750
x = -225 + 750
x = 525
Therefore, if the price per item is $1.50, the manufacturing company will sell 525 items.