Question

Compare the y-intercepts and the rates of change of the following items.

Answer 1

The y-intercepts are the same, but the rates of change are different.

Answer 2

Answer:  The correct option is

(C) The y-intercepts are the same, but the rates of change are different.

Step-by-step explanation:  We are given to compare the y-intercepts and the rates of change of the given items.

For item I :

The given equation of the line is in slope-intercept for, as follows :

$y=2x-4.$

So, the y-intercept of the line is -4 and the rate of change is given by the slope of the line, i.e., 2.

For item II :  

We see that

at x = 0, the value of y is -4. So, the y-intercept of the linear function (a line) is -4.

Now, (-4, -6) and (-2, -5) are two points on the line, so the rate of change will be

$R=\dfrac{-5-(-6)}{-2-(-4)}=\dfrac{1}{2}.$

Therefore, the y-intercepts are same but rate of changes are different.

Thus, (C) is the correct option.