Question

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school. What does the slope of the graph mean? Tracie’s bus travels towards her home at an average speed of mile per minute. Tracie’s bus travels towards her home at an average speed of 2 miles per minute. Tracie’s bus travels away from her home at an average speed of mile per minute. Tracie’s bus travels away from her home at an average speed of 2 miles per minute.

Answer 1

Answer:

1. Tracie's bus travels towards her home at an average speed of $\frac{1}{2}$ miles per minute.

Step-by-step explanation:

From the graph, we see that,

X-axis represents the time (in minutes) and the Y-axis represents the distance from home (in miles).

Also, the graph of the function is decreasing by 1 miles for every 2 minutes.

That is, the distance from home is decreasing as the time increases.

That is, the bus is getting closer to the home.

Further, as the distance is decreasing by 1 mile for every 2 minutes.

Thus, the rate of decrease is $\frac{1}{2}$ miles per minute.

As we know, $Speed=\frac{Distance}{Time}$

So, the slope represents the speed of the bus travelling towards home.

That is, 'Tracie's bus travels towards her home at an average speed of $\frac{1}{2}$ miles per minute'.

Answer 2

The slope of the graph is -0.5, and it shows that the velocity of the bus is -0.5 miles/min and is therefore slowing down.

How to measure the rate of change of something as some other value changes?

Suppose that we have to measure the rate of change of y as x changes, then we have:

$Rate = \dfrac{y_2 - y_1}{x_2 - x_1}$

where we have

$\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2$

Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)

For a straight line, the slope of that line is the rate of increment of its output based on the input(the horizontal axis) usually.

Now, since in the considered graph, we have the x-axis as the axis for time measurement, and the y-axis as the axis for the distance measurement from home (by the bus):

Thus, we get:
Slope = Rate = $\dfrac{\text{Difference in corresponding distance values}}{\text{Difference in time values}}$ = velocity of the bus

Taking any two different time, at t = 2 seconds and at t = 4 seconds, we get the distance as 8 miles from home, and 7 miles from home respectively.

Thus, we get:

Velocity of the bus = $\dfrac{7 - 8}{4 -2 } = -\dfrac{1}{2} = -0.5 \: \rm miles/min$

(there is difference between speed and velocity of an object)

The negative sign shows that the bus is slowing down. And as the time increases, the distance from home decreases, therefore, the bus is reaching to the home.

Learn more about average speed here:

https://brainly.com/question/12322912