The price of an airplane ticket for a return trip is $600. The airline company attracts an average 500 daily bookings at this price. It has been observed that there is a linear relationship between the price of the return trip and the number of bookings. This is such that for every $50 decrease in price, there is an additional 100 bookings. Form a linear equation that relates the number of bookings with the price of the ticket.

The problem describes a linear relationship between the price of the return trip (which we'll denote as P) and the number of bookings (which we'll denote as B).

We know that when the price is $600, the number of bookings is 500. This gives us one point on the line: (P1, B1) = (600, 500).

We also know that for every $50 decrease in price, there is an additional 100 bookings. This gives us the slope of the line (m). The slope of a line is change in y divided by change in x. Here, y is the number of bookings and x is the price. So, m = ΔB / ΔP = 100 / -50 = -2.

Now we can use the point-slope form of a linear equation to write our equation: B - B1 = m(P - P1).

Substituting our known values, we get: B - 500 = -2(P - 600).

Solving for B, we get: B = -2P + 1200 + 500.

So, the linear equation that relates the number of bookings with the price of the ticket is: B = -2P + 1700.

The problem describes a linear relationship between the price of the ticket (P) and the number of bookings (B). We know that when the price is $600, the number of bookings is 500. This gives us one point on the line: (P1, B1) = (600, 500).

We also know that for every $50 decrease in price, there is an additional 100 bookings. This means that the slope of the line (m) is -100/50 = -2. This is because the slope of a line is defined as the change in y (in this case, bookings) divided by the change in x (in this case, price), and we know that when the price decreases by$50 (a change of -50), bookings increase by 100 (a change of +100).

The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is 0). In this case, we want to write an equation in the form B = mP + b.

We already know that m = -2. To find b, we can substitute the known point (P1, B1) = (600, 500) into the equation and solve for b:

500 = -2*600 + b 500 = -1200 + b b = 500 + 1200 = 1700

So the equation that relates the number of bookings with the price of the ticket is B = -2P + 1700.