Question

Function 1: y = 4x + 5

Function 2: The line passing through the points (1, 6) and (3, 10).

Which of these functions has the greater rate of change?
A) Function 1, because the slope is 5 and the slope of function 2 is 4.
B) Function 1, because the slope is 4 and the slope of function 2 is 2.
C) Function 2, because the slope is 7 and the slope of function 1 is 5.
D) Function 2, because the slope is 5 and the slope of function 1 is 4.

Answer 1

B) Function 1, because the slope is 4 and the slope of function 2 is 2.

Explanation:

Function 1 is in slope-intercept form, which is

y = mx+b, where m is the slope and b is the y-intercept.

This means the slope of function 1 is 4.

The slope of function 2 is given by the formula

`m=(y_2-y_1)/(x_2-x_1)`

Using our two points for function 2, we have

m = (10-6)/(3-1) = 4/2 = 2

This means the slope of function 1 is greater.

Answer 2

B. The formula for function 2 is y = 2x + 4