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

The items have different y-intercepts and different rates of change.

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

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

The items have the same y-intercept and the same rate of change.

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-12-27T07:02:36-05:00

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

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ColinJacobus ColinJacobus · Answer 2 · 2019-06-02T23:30:23-04:00

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.