When the owner of a gas station sets the price of 1 gallon of unleaded gasoline at 2$, he can seek approximately 20,000 gallons per day. When he sets the price of gas at 5$ per gallon, he can sell approximately 14,000 gallons per day. Let G(x) denote the number of gallons of unleaded gasoline per day when the price is x dollars. Assume that G(x) is a linear function of x. Approximately how many gallons will be sold per day if the price of gasoline is 2.50$ per gallon?

To find out approximately how many gallons will be sold per day when the price of gasoline is $2.50 per gallon, we can use the concept of a linear function.

A linear function can be represented by a straight line on a graph, where the price of gasoline (x) is on the x-axis and the number of gallons sold (G(x)) is on the y-axis.

We are given two points on this line:
- When the price is $2 per gallon, the owner can sell approximately 20,000 gallons per day.
- When the price is $5 per gallon, the owner can sell approximately 14,000 gallons per day.

Let's use these two points to find the slope (rate of change) of the line:

Slope (m) = (G(x2) - G(x1)) / (x2 - x1)

Here, x1 = 2 (price in dollars) and G(x1) = 20,000 (gallons per day)
And, x2 = 5 (price in dollars) and G(x2) = 14,000 (gallons per day)

Substituting these values into the slope formula:

m = (14,000 - 20,000) / (5 - 2)
= -6,000 / 3
= -2,000

The negative sign indicates that the number of gallons sold decreases as the price increases.

Now that we have the slope, we can use the point-slope form of a linear equation to find an equation for G(x):

G(x) - G(x1) = m(x - x1)

Substituting the values, we have:
G(x) - 20,000 = -2,000(x - 2)

Simplifying this equation gives:
G(x) - 20,000 = -2,000x + 4,000

Rearranging the equation to solve for G(x), we have:
G(x) = -2,000x + 24,000

Now we can substitute x = 2.50 into the equation to find the approximate number of gallons sold when the price is $2.50 per gallon:

G(2.50) = -2,000(2.50) + 24,000
= -5,000 + 24,000
= 19,000

Therefore, approximately 19,000 gallons will be sold per day if the price of gasoline is $2.50 per gallon.

To find the approximate number of gallons that will be sold per day when the price of gasoline is $2.50 per gallon, we need to determine the equation of the linear function G(x) that relates the number of gallons sold to the price.

First, let's find the slope of the linear function by using the given data points:

Slope (m) = (change in gallons) / (change in price)
m = (14,000 - 20,000) / (5 - 2)
m = -6,000 / 3
m = -2,000

Now that we have the slope, we can determine the equation of the linear function using the point-slope form:

y - y1 = m(x - x1)

Using the point (2, 20,000) as our reference point:

G(x) - 20,000 = -2,000(x - 2)

Simplifying the equation:

G(x) - 20,000 = -2,000x + 4,000

G(x) = -2,000x + 24,000

Now we can substitute the price of $2.50 into the equation to find the approximate number of gallons sold:

G(2.50) = -2,000(2.50) + 24,000
G(2.50) = -5,000 + 24,000
G(2.50) = 19,000

Therefore, approximately 19,000 gallons will be sold per day if the price of gasoline is $2.50 per gallon.

you have a line containing the points

(2,20) and (5,14)

where y is 1000's of gallons of gas at price x.

So, just use your two-point form for the line, and then find y(2.50).