Question

A hot-air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height of the balloon and let x represent the number of minutes the balloon descends.

(a) Write an equation that relates the height of the hot-air balloon and the number of minutes it descends.
(b) Sketch the graph of the equation.
(c) What is the y-intercept of the graph, and what does it represent in the context of the problem?

Answer 1

The equation relating the height of the hot-air balloon and the number of minutes it descends is y = 1120 - 80x. The y-intercept of the graph is (0, 1120) and represents the initial height of the balloon.

Step-by-step explanation:

(a) The equation that relates the height of the hot-air balloon (y) and the number of minutes it descends (x) is y = 1120 - 80x.

(b) To sketch the graph of the equation, we plot the points on a coordinate plane by substituting different values of x into the equation and finding the corresponding values of y. We can choose any x values, but it's usually a good idea to choose values that make the equation easy to solve. For example, if we substitute x = 0, we get y = 1120 - 80(0) = 1120. So, the y-intercept is (0, 1120). We can then choose another value of x, such as x = 1, to find another point on the graph.

(c) The y-intercept of the graph is the point (0, 1120). In the context of the problem, it represents the initial height of the hot-air balloon.