Function A is represented by the equation y = 3x + 4.
Function B is a linear function that goes through the points shown in the table.
Which statement correctly compares the rates of change of the two functions?
A. The rate of change of function A is 4.
The rate of change of function B is 5.
B. The rate of change of A is 3.
The rate of change of B is 10.
C. The rate of change of function A is 3.
The rate of change of function B is 5.
D. The rate of change of function A is 4.
The rate of change of function B is 10.
Thanks! :D
Function B is a linear function that goes through the points shown in the table.
Which statement correctly compares the rates of change of the two functions?
A. The rate of change of function A is 4.
The rate of change of function B is 5.
B. The rate of change of A is 3.
The rate of change of B is 10.
C. The rate of change of function A is 3.
The rate of change of function B is 5.
D. The rate of change of function A is 4.
The rate of change of function B is 10.
Thanks! :D
Answers & Comments
Step-by-step explanation:
To compare the rates of change of the two functions, we need to find the slope of each function.
For function A, the equation is y = 3x + 4. This is in slope-intercept form, where the coefficient of x is the slope. Therefore, the slope of function A is 3.
For function B, we can use the points in the table to find the slope. The slope of a line passing through two points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). Using the points in the table, we get:
Slope of function B = (7 - 2) / (2 - (-1)) = 5/3
Therefore, the statement that correctly compares the rates of change of the two functions is:
C. The rate of change of function A is 3.
The rate of change of function B is 5/3.