t has been discovered in a certain state that the relationship between the number of snow shovels demanded varies linearly with its price.

When the price per item was $ 38 ,2200 items were demanded;
When the price was $ 49 , 2125 items were demanded.

Determine the price per item when 2143 snow shovels are demanded. $
Above what price will the demand be zero ? $

treat the data as two ordered pairs, and find the linear equation

(38, 2200) and (49,2125)
slope = (2125-2200)/(49-38) = -75/11

so s - 2200 = (-75/11)(p-38)

11s - 24200 = -75p + 2850
11s + 75p = 27050

when s = 2143,
11(2143) + 75p = 27050
75p = 3477
p = $46.36

when s = 0
0 + 75p = 27050
p = $360.67

thank you so much!!!

To determine the price per item when 2143 snow shovels are demanded, we can use the concept of linear relationships. The given information states that the relationship between the number of snow shovels demanded and its price is linear.

We are given two data points, which we can use to form a linear equation. Let's denote the number of snow shovels demanded as "x" and the price per item as "y."

Using the first data point:
When the price per item was $38, 2200 items were demanded.
So, we have the first point (38, 2200).

Using the second data point:
When the price per item was $49, 2125 items were demanded.
So, we have the second point (49, 2125).

Now, we can use these two points to find the equation of the linear relationship. The equation of a linear relationship can be written in the form y = mx + b, where "m" represents the slope and "b" represents the y-intercept.

To find the slope (m), we can use the formula:
m = (change in y) / (change in x)

Using the given data points:
m = (2125 - 2200) / (49 - 38)
m = -75 / 11
m ≈ -6.82

Now, let's substitute the slope and one of the data points into the equation y = mx + b to solve for the y-intercept (b).

Using the first data point:
2200 = (-6.82)(38) + b
2200 = -259.16 + b
b = 2459.16

Therefore, the equation of the linear relationship is:
y = -6.82x + 2459.16

To determine the price per item (y) when 2143 snow shovels are demanded (x = 2143), we can substitute x = 2143 into the equation and solve for y.
y = -6.82(2143) + 2459.16
y ≈ $24.12 (rounded to two decimal places)

So, the price per item when 2143 snow shovels are demanded is approximately $24.12.

To determine the price at which the demand will be zero, we need to find the x-value (number of snow shovels demanded) when y (price per item) is equal to zero.

Setting y = 0 in the equation:
0 = -6.82x + 2459.16
6.82x = 2459.16
x ≈ 360.10 (rounded to two decimal places)

Therefore, the number of snow shovels demanded will be zero when the price per item is above approximately $360.10.