# How do I found the value of b? The answer is 4.7×10^4 to 5.3×10^4

May 10, 2018

b should be the gradient of the line.

#### Explanation:

As $y = m x + c$, and we know that $p = y$ and $x = \left(\frac{1}{H}\right)$, then $b$ must be the gradient of the line.

We can use the gradient formula, if we use 2 points from the graph:

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = m$

I will choose the points $4 , 2.0 \times {10}^{5}$=${x}_{2} , {y}_{2}$
and
$2 , 1.0 \times {10}^{5}$=${x}_{1} , {y}_{1}$

Plug everything in:

$\frac{\left(2.0 \times {10}^{5}\right) - \left(1.0 \times {10}^{5}\right)}{4 - 2} = \frac{10 000}{2} = 50000 = 5.0 \times {10}^{4}$- which is within the acceptable range.

When it comes to the unit of $b$:

$y$ has a unit of Pascals, $P a = \frac{F}{A} = N {m}^{-} 2 = \frac{k g m {s}^{-} 2}{{m}^{2}} = \left(k g {m}^{-} 1 {s}^{-} 2\right)$

while $x$ has a unit of ${m}^{-} 1$, so we must multiply it by $k g {s}^{-} 2$ to get to the correct unit. as $y = m x$

So the unit for $b$ is $k g {s}^{-} 2$- which could be written as $P a \times m$. (Which is still equivalent to $k g {s}^{-} 2$).