Assume that the situation described can be modeled by a linear equation. Use the given information to find the y=mx+b form of the equation of the line. Suppose that a sales person observes that if an item is priced at $4 per item then 11 items are sold. If 9 items are sold for $6 per item then find an equation to model the number y of items sold for x dollars per item.
slope (m) = (9-11)/(6-4) = -1
so, y=-x+b
y(4)=11, so b=15
y = -x+15
To find the equation of the line in the form y = mx + b using the given information, we need to determine the values of m and b.
Let's start by finding the value of m, which represents the slope of the line. The slope represents the change in y divided by the change in x.
Given that when the price is $4 per item, 11 items are sold, we can use this as one point on the line: (4, 11).
Given that when the price is $6 per item, 9 items are sold, we can use this as another point on the line: (6, 9).
Now, we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (9 - 11) / (6 - 4)
m = -2 / 2
m = -1
Now that we have the value of m, we can proceed to find the value of b, which represents the y-intercept of the line. The y-intercept is the value of y when x = 0.
To find the value of b, we can use one of the points we have already identified, let's use (4, 11):
y = mx + b
11 = -1 * 4 + b
11 = -4 + b
b = 11 + 4
b = 15
Therefore, the equation of the line that models the number of items sold (y) for x dollars per item is:
y = -x + 15