Two linear functions are shown below.
Function A: y = 8x - 2
Function B:
x -1 0 1 2
y -2 -1 0 1
Which statement is true?
Responses
A The y-intercept of function A is equal to the y-intercept of Function B.The y -intercept of function A is equal to the y -intercept of Function B.
B The y-intercept of function A is less than the y-intercept of Function B.The y -intercept of function A is less than the y -intercept of Function B.
C The y-intercept of function A is greater than the y-intercept of Function B.The y -intercept of function A is greater than the y -intercept of Function B.
D The rate of change for Function A is equal to the rate of change for function B.
The correct answer is D. The rate of change for Function A is equal to the rate of change for Function B.
To find the rate of change for a linear function, we can look at the slope of the line.
For Function A, the slope is 8. This means that for every 1 unit increase in x, there is an 8 unit increase in y.
For Function B, we can calculate the slope using the given points. The slope between (-1, -2) and (0, -1) is 1. The slope between (0, -1) and (1, 0) is also 1. The slope between (1, 0) and (2, 1) is also 1. This means that for every 1 unit increase in x, there is a 1 unit increase in y.
Since the slopes of both functions are equal to 1, the rate of change for Function A is equal to the rate of change for Function B.