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
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{3000-1000}{206-210} \\ =\frac{2000}{-4} \\ =-500 \end{gathered}[/tex]
Hence, m=-500.
Take any one point and the slope, (210,1000) , m=-500
The point slope form is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1000=-500(x-210) \end{gathered}[/tex]
When, the altitude is 6000 ft, then substitute y=6000 in the above equation we get,
[tex]\begin{gathered} 6000-1000=-500(x-210) \\ 5000=-500(x-210) \\ (x-210)=\frac{5000}{-500} \\ (x-210)=-10 \\ x=210-10 \\ x=200 \end{gathered}[/tex]
Hence, if an altitude is of 6000 ft, then the boiling point is 200 degree farenheit.
