Question

we measure the atmospheric pressure and the boiling - point of water. we measure the pressure in kilopascals (kpa) and the boiling point in degrees celsius (°c). at a pressure of 100 kpa the boiling point of water is 100°c and drops by about 3.75°c for each 10 kpa drop in atmospheric pressure. find a linear function g that relates them. also, find the boiling point of water (in °c) if the atmospheric pressure is 74 kpa.

Explanation:

Step1: Determine the slope of the linear - function

The boiling - point drops by about $3.75^{\circ}C$ for each $10$ kPa drop in pressure. So the slope $m$ of the linear function $y = mx + b$ (where $y$ is the boiling - point and $x$ is the pressure) is $m=-\frac{3.75}{10}=- 0.375$.

Step2: Determine the y - intercept

When the pressure $x = 100$ kPa, the boiling - point $y = 100^{\circ}C$. Substitute $x = 100$, $y = 100$, and $m=-0.375$ into $y=mx + b$. We get $100=-0.375\times100 + b$. Then $100=-37.5 + b$, and $b = 100 + 37.5=137.5$.

Step3: Write the linear function

The linear function is $q(x)=-0.375x + 137.5$.

Step4: Find the boiling - point at 74 kPa

Substitute $x = 74$ into $q(x)=-0.375x + 137.5$. Then $q(74)=-0.375\times74 + 137.5=-27.75+137.5 = 109.75^{\circ}C$.

Answer:

$109.75^{\circ}C$