Suppose that a sales person observes that if an item is priced at $3 per item then 11 items are sold. If 9 items are sold for $5 per item then find a liner equation to model the number y of items sold for x dollars per item. Find the slope intercept form of the equation of the line.
Butch has fifty vinyl records from the fifties, including exactly on Smiley Lewis two by the Drifters, Three by Bobby Darin, four by the Coasters, and five by Fats Domino. if he randomly selects one from his collection of fifty, find the probability it will be the following.
a) The Drifters
b) The Coasters
To find the linear equation that models the relationship between the number of items sold and the price per item, we can use the slope-intercept form of a linear equation:
y = mx + b
Where:
y = dependent variable (number of items sold)
x = independent variable (price per item)
m = slope of the line
b = y-intercept of the line
Let's find the values of m and b using the given information:
For the first scenario, when the price per item is $3 and 11 items are sold, we have:
x₁ = 3 (price per item)
y₁ = 11 (number of items sold)
For the second scenario, when the price per item is $5 and 9 items are sold, we have:
x₂ = 5 (price per item)
y₂ = 9 (number of items sold)
We can now calculate the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given values, we get:
m = (9 - 11) / (5 - 3)
m = -2 / 2
m = -1
Next, we can calculate the y-intercept (b) using the formula:
b = y - mx
Taking one of the points (x₁, y₁), we have:
b = y₁ - m * x₁
b = 11 - (-1) * 3
b = 11 + 3
b = 14
Therefore, the linear equation that models the number of items sold (y) for the price per item (x) is:
y = -x + 14
This is the slope-intercept form of the equation.