William is in the middle of swimming in a ten-mile race. He swims at a steady speed, and then slows down, stops to eat, swims faster to get back in the race, and returns to a steady speed. He later stops for water, and then again swims faster to get back in the race. Which graph best represents the situation? A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, increases, is constant, decreases to 0, and then increases.

A graph with time on the x-axis and speed on the y-axis. The graph decreases, is constant at 0, increases, is constant, decreases to 0, and then increases.

A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, is constant, increases, decreases to 0, and then increases.

A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, is constant, increases, and then is constant.

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  A

Step-by-step explanation:

The attachment shows the description of the swimmer's activity as given in the problem statement, and compares it to the descriptions of the graphs that have the closest match.

As you can see, neither graph description matches exactly. If we assume that "stops to eat" and "stops for water" do not mean the speed stayed zero long enough to be "constant", then graph choice A (the first one) seems the best match.

Step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: