Question

I understand how to put it in point-slope form and how to solve it! I don’t understand how to get the points that are used in the equation. If that makes sense.

Answer 1

It is given that,

At an altitude of 1000 ft, water boils at 210 degree farenheit.

At an altitude of 3000 ft, water boils at 206 degree farenheit.

Let x be the boiling point and y be altitude.

To find the point-slope form:

Let find the slope first,

Using the two points are, (210,1000) and (206,3000)

So, the slope is

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ =(3000-1000)/(206-210) \\ =(2000)/(-4) \\ =-500 \end{gathered}`

Hence, m=-500.

Take any one point and the slope, (210,1000) , m=-500

The point slope form is,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-1000=-500(x-210) \end{gathered}`

When, the altitude is 6000 ft, then substitute y=6000 in the above equation we get,

`\begin{gathered} 6000-1000=-500(x-210) \\ 5000=-500(x-210) \\ (x-210)=(5000)/(-500) \\ (x-210)=-10 \\ x=210-10 \\ x=200 \end{gathered}`

Hence, if an altitude is of 6000 ft, then the boiling point is 200 degree farenheit.