Answer
(a) $y = \frac{4.34}{10}x + 15$
(b) $196$ ft
Work Step by Step
(a) At 0 ft of descent (ie. the surface), the water pressure is $15$ $lb/in^{2}$. Thus, that is the y-intercept for the graph of water pressure as a function of depth below the ocean surface, or $b$.
For every 10 ft, the water pressure increases by $4.34$ $lb/in^{2}$, so $m$ must be such that when $x$ is 10, $mx$ is $4.34$. Thus, $m= \frac{4.34}{10}$.
The function is then:
$y = \frac{4.34}{10}x + 15$
(b) When the pressure is $100$ $lb/in^{2}$, $y = 100$. Inputting this into the equation gives:
$100 = \frac{4.34}{10}x +15$
$85 = \frac{4.34}{10}x$
$85 \div \frac{4.34}{10} = x$
$x \approx 196$ ft
