Question

Function A is represented by the equation y=-2x + 1.Function B is a linear function that goes through the points shown inthe table.x 1346y 19 13 21Which statement correctly compares the rates of change of the twofunctions?O A. The rate of change of function A is-2The rate of change of function B is 4.O B. The rate of change of function A is 1.The rate of change of function B is 8.C. The rate of change of function A is 1.The rate of change of function B is 4.D. The rate of change of function A is-2The rate of change of function B is 8.

Answer 1

In linear functions, the rate of change is equivalent to the slope of the line. In function A we already now the slope intercept equation, which means that we already now the slope of the function.

In this case, the slope of function A is -2 so is the rate of change.

To find the rate of change of function B, we need to use 2 of the ordered pairs in the formula to find the slope of a line:

$m=\frac{y2-y1}{x2-x1}$

Let's choose two of the given ordered pairs and replace for them in the formula. We are going to use (1,1) and (3,9):

$m=\frac{9-1}{3-1}=\frac{8}{2}=4$

The slope of function B is 4 so is the rate of change.

In conclusion, the correct choice is A. The rate of change of function A is -2. The rate of change of function B is 4.