Question

an unknown metal has been found and the following experimental results have been tabulated in the table below. the table contains the grams of the unknown metal and the volume in milliliters of water displacement. find a linear model that express volume as a function of the mass.
round your answers to 3 decimal places

grams	volume in ml
22.5	260.3
24	277.6
25.5	295
27	312.3
28.5	329.7
30	343.6

volume = x+ where x is the grams of the unknown metal

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Explanation:

Step1: Recall linear - equation form

The linear equation is $y = mx + b$, where $y$ is volume, $x$ is mass. The slope $m=\frac{\Delta y}{\Delta x}$.

Step2: Select two points

Let's take $(x_1,y_1)=(21,233.4)$ and $(x_2,y_2)=(22.5,260.3)$.

Step3: Calculate the slope $m$

$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{260.3 - 233.4}{22.5 - 21}=\frac{26.9}{1.5}\approx17.933$.

Step4: Find the y - intercept $b$

Substitute $m = 17.933$, $x = 21$, and $y = 233.4$ into $y=mx + b$.
$233.4=17.933\times21 + b$.
$b=233.4-17.933\times21$.
$b=233.4 - 376.593=-143.193$.

Answer:

Volume $=17.933x - 143.193$