Question

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?

Answer 1

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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 `10x` which reduces 3000 in relation to time `x`. Consequently 3000 feet must be the initial height. it is also the y-intercept.

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

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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.
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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.
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`color(blue)("To determine the time to reach ground level.")`

Set `y=0` giving

`0=-10x+3000`

`=>+10x=3000`

`color(blue)(x=3000/10 = 300" seconds" -> 5" minutes exactly")`