Question

The table and the graph represent the rate at which two machines arebottling milk in gallons per second.

Answer 1

Given:

There are given the information about the two machines, one is in table form and another is in the graph.

Explanation:

We need to find the rate of change from both of the machines.

So,

For machine 1:

Choose two-point and find the slope by using the slope formula:

So,

The points are;

$(1,0.6),and,(2,1.2)$

From the formula to find the rate of change:

$r=\frac{y_2-y_1}{x_2-x_1}$

Then,

$\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{1.2-0.6}{2-1} \\ r=\frac{0.6}{1} \\ r=0.6 \end{gathered}$

Now,

For machine 2:

We need to choose two points from the graph.

So,

Two points are:

$(8,6),and,(16,12)$

Then,

From the formula:

$\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{12-6}{16-8} \\ r=\frac{6}{8} \\ r=0.75 \end{gathered}$

Final answer:

Hence, the machine 2 is faster at botting milk because the value of the rate of machine 2 is greater than the value of rate of machine 1.