Question

At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an altitude of 1000 feet, water boils at 210°F. At an altitude of 3000 feet, water boils at 206°F. Use an equation in point-slope form to find the boiling point of water at an altitude of 8000 feet. Solve the problem using an equation in point-slope form.

Answer 1

the boiling point of water at an altitude of 8000 feet is 196°F

Explanation:

Answer 2

Let's assume

boiling point is y

altitude is x

we are given

This relationship between altitude and boiling point is linear

At an altitude of 1000 feet, water boils at 210°F

so, first point is (1000,210)

so, x1=1000 , y1=210

At an altitude of 3000 feet, water boils at 206°F

so, second point is (3000,206)

so, x2=3000,y2=206

now, we can find slope

`m=(y_2-y_1)/(x_2-x_1)`

now, we can plug values

`m=(206-210)/(3000-1000)`

`m=-(1)/(500)`

now, we can use point slope form of line

`y-y_1=m(x-x_1)`

so, we can plug it

`y-210=-(1)/(500)(x-1000)`

so, point slope form of line is

`y-210=-(1)/(500)(x-1000)`

now, we can plug x=8000

and then we can solve for y

`y-210=-(1)/(500)(8000-1000)`

`y=196`

So,

the boiling point of water at an altitude of 8000 feet is 196°F..........Answer