# A skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is y=-10x+3000, how do you graph and Interpret the x-intercept and the slope?

Nov 12, 2016

See description

#### Explanation:

You have to try and understand what the numbers are doing and associate that with actual events.

It is stated that $y$ is height 'above ground' . If he goes 'below ground than he is in trouble!

The right hand side (RHS) has negative $10 x$ which reduces 3000 in relation to time $x$. Consequently 3000 feet must be the initial height. it is also the y-intercept.

The $- 10 x$ has to be the count of feet as the parachutist descends in $x$ seconds. It is also the slope (gradient) of the graph.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
At the point where the graph crosses the x-axis it means that $y = 0$ and $y$ is the height above ground.

Consequently the x-intercept is at the point of reaching the ground.

The slope is the rate of descent which is constant as time (x) increases.
..................................................................................................................
Actually the rate of descent is a very rounded value. To 2 decimal places I think it is 9.81 metres per second per second in metric form.

In imperial form it is something like 32.2 feet per second per second.
....................................................................................................................

$\textcolor{b l u e}{\text{To determine the time to reach ground level.}}$

Set $y = 0$ giving

$0 = - 10 x + 3000$

$\implies + 10 x = 3000$

$\textcolor{b l u e}{x = \frac{3000}{10} = 300 \text{ seconds" -> 5" minutes exactly}}$