Question

Modeling with Linear Functions
When a diver descends a depth of 9 feet below the surface, the pressure is 18.7 pounds per square inch. At a depth of 14 feet, the pressure is 20.9 pounds.The pressure increases linearly at a constant rate as the diver descends.
Question 1
Which function models the amount of pressure, y, in pounds per square inch at a depth of x feet?
Responses
A y = 3.96x + 2.2y = 3.96x + 2.2
B y = 2.2x + 1.1y = 2.2x + 1.1
C y = 0.72x + 14.74y = 0.72x + 14.74
D y = 0.44x + 14.74y = 0.44x + 14.74
Question 2
To the nearest tenth, determine the pressure per square inch at a depth of 25 feet.
Responses
A 22.5 pounds per square inch22.5 pounds per square inch
B 25.7 pounds per square inch25.7 pounds per square inch
C 27.9 pounds per square inch27.9 pounds per square inch
D 30.5 pounds per square inch

Answer 1

To solve the questions, we first need to determine the linear function that relates pressure (y) to depth (x).

### Question 1

We are given two data points:
1. At a depth of \(x = 9\) feet, \(y = 18.7\) pounds per square inch.
2. At a depth of \(x = 14\) feet, \(y = 20.9\) pounds per square inch.

First, we can find the slope (\(m\)) of the linear function using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20.9 - 18.7}{14 - 9} = \frac{2.2}{5} = 0.44
\]

Now that we have the slope, we can use one of the points to find the y-intercept (\(b\)) using the slope-intercept form of a line, \(y = mx + b\).

Using the point (9, 18.7):

\[
18.7 = 0.44(9) + b
\]
\[
18.7 = 3.96 + b
\]
\[
b = 18.7 - 3.96 = 14.74
\]

Now we have the linear function:

\[
y = 0.44x + 14.74
\]

Thus, the answer to Question 1 is:

**D) \(y = 0.44x + 14.74\)**

### Question 2

Now, we need to determine the pressure at a depth of 25 feet using the function we derived:

\[
y = 0.44(25) + 14.74
\]
\[
y = 11 + 14.74 = 25.74
\]

To the nearest tenth, the pressure per square inch at a depth of 25 feet is:

**B) 25.7 pounds per square inch**