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This graph tracks the distance travelled from home over an 8 hour time period. Which of the following is NOT the rate of change for one of the legs(A, B, C, D, or E) shown above? A. 0B. 80C. 40D. -60

This Graph Tracks The Distance Travelled From Home Over An 8 Hour Time Period Which Of The Following Is NOT The Rate Of Change For One Of The LegsA B C D Or E S class=

Sagot :

The question is about the rate of change of the graph, out of the options we need to find the option that is not a slope of the lines that compose the graph. Since it is a graph that is composed by multiple lines, we can analyze the rate of change for each line. In this case, the rate of change correspond to the slope of the line, which at the same time, tells us "how much" the values in the y axis changes as the x-axis changes. In here, we denote a change positive if the value of the axis increases and negative if the change in the axis is negative.

Consider, for instance, part A of the graph.

Note that this part goes from hour 0 to hour 2. So, in the x axis the variable increased in 2 units. That is, a positive change. Now, noticed that at hour 0 the value of distance was 0. After two hours, the distance was 80. Then, the value in y increased in 80. So, in this case we have a positive change. Now, to calculate the rate of change in this part, we divide the change of Y by the change of X.

That is, 80/2, which is 40. In this case, the rate of change for the part A is 40.

For part B,

note that at hour 2 we are at 80, and then at hour 3 we are at 80. In this case, the change in the x axis is still 1 unit. However, the change in y is 0, since we are at 80 at time 2 and at time 3. So the slope of this part is the change of y, divided by the change in x, which is 0/1 =0.

Using this principle, we can determine that D has also a rate of change of 0.

Now, let us continue with part C.

Note that at time 3, we are at 80. Then, at time 4 we are at 120. In the x-axis the cahnge was of 1 unit. In the case of Y, we changed from 80 to 120. That is, the change was 120-80 =40. So, in this case, the slope is the change in y (40) divided by the change in x (1). That is 40/1 = 40. So part C also has a rate of change of 40.

Finally, we will calculate the rate of change for part E. At time 6, we are at 120 and at time 8 we are at 0. In the x axis, we got from 6 to 8. So it is an increase of 2 units. In Y, however, we go from 120 to 0. That is, we decrease in 120 units. Since it is a decrease, we consider this a change of -120.

So, the rate of change would be the change in y (-120) divided by the change in x (2). So the rate of change of E is -120/2 = -60. So the rate of change for E is -60.

Then, the only correct option is B. 80, since no line in the graph has that rate of change.

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