Question

A remote control airplane descends at a rate of 3 feet per second. after 6 seconds the plane is 89 feet above the ground. which equation models this situation and what is the height of the plane after 12 seconds?

y-89= -3(x-6) ; 71 feet.

I just don't understand how they got that equation.

Answer 1

ur looking at point slope form of an equation : y - y1 = m(x - x1)
ur slope is -3/1 or just -3, because the plane descends...it goes down. ur points are (6,89)...so ur x axis is seconds and ur y axis is feet.

6 = y1 and 89 = y2....ur slope(m) = -3.
y - y1 = m(x - x1)......after 12 seconds....seconds = x
y - 89 = -3(12 - 6)
y - 89 = -3(6)
y - 89 = -18
y = -18 + 89
y = 71

so after 12 seconds (x), ur plane is at 71 ft (y)

Answer 2

Explanation:

In this question descending height of an airplane, when plotted on a graph shows a straight line.

So the linear graph will represent y - y ' = m(x - x')

where y represents the height and x represents the time.

Remote control airplane descends at a rate of 3 feet per second.

This represents rate of decrease in the height = m (slope of the line) = -3 (minus notation is because height is decreasing)

Now it is given that airplane is at 89 feet above the ground after 6 seconds.

That means line passes through a point (6, 89).

By putting these values in the equation

y - 89 = -3(x - 6)

We have to find the height of the airplane after x = 12 seconds.

y - 89 = -3(12 - 6)

y - 89 = -18

y = 89 - 18

y = 71 feet.