The table represents a function. x y −1 0 2 3 3 4 5 6 complete the statement by selecting from the drop-down menu. the rate of change in the function y=2x+5 is the rate of change of the function represented in the table. a. greater than b. less than c. equal to

The rates of the two functions are to be compared.

The rate of change of the second function is A. greater than the rate of change of the function represented in the table.

The rate of the first function is given by

In the equation of a line

m = Rate

c = y intercept

The second function is

The rate is of the function is

So, the rate of change of the second function is greater than the rate of change of the function represented in the table.

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A) Greater than

The equation y = 2x+5 has a greater rate of change compared to the table.

Pick any two points from the table. I'm going to pick the first two rows so I picked (-1,0) and (2,3) as the two points. From here, the idea is to use the slope formula

m = (y2 - y1)/(x2 - x1)

m = (3-0)/(2 - (-1))

m = (3 - 0)/(2 + 1)

m = 3/3

m = 1

The slope of the line going through all of the points shown in the table is m = 1. So the rate of change for the table is also 1.

The slope of y = 2x+5 is m = 2. The equation y = 2x+5 is in the form y = mx+b. So the rate of change for y = 2x+5 is 2.

Comparing the table's rate of change to the equation's rate of change, we see that the equation's rate of change is larger.

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