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.

Step-by-step 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=(y_2-y_1)/(x_2-x_1)`

Then,

`\begin{gathered} r=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ r=(1.2-0.6)/(2-1) \\ r=(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=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ r=(12-6)/(16-8) \\ r=(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.