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QuestionWhat represents the average speed of a cat at point AA on a graph: xx-coordinate, yy-coordinate, slope, or distance?

Studdy Solution

STEP 1

Assumptions1. Point AA represents the end point of the cat's journey. . The xx-coordinate of point AA represents the total time taken.
3. The yy-coordinate of point AA represents the total distance traveled.
4. The average speed is defined as the total distance traveled divided by the total time taken.

STEP 2

We need to find the average speed of the cat. According to the definition, the average speed is the total distance traveled divided by the total time taken.
Average speed=Total distance traveledTotal time takenAverage\, speed = \frac{Total\, distance\, traveled}{Total\, time\, taken}

STEP 3

From the assumptions, we know that the xx-coordinate of point AA represents the total time taken and the yy-coordinate of point AA represents the total distance traveled. So, we can rewrite the formula for average speed as followsAverage speed=y coordinate of point Ax coordinate of point AAverage\, speed = \frac{y\, coordinate\, of\, point\, A}{x\, coordinate\, of\, point\, A}

STEP 4

The slope of a line through two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given by the formulalope=y2−y1x2−x1lope = \frac{y2 - y1}{x2 - x1}

STEP 5

In our case, the two points are AA and (0,0)(0,0). So, the slope of the line through AA and (0,0)(0,0) islope=y coordinate of point A−0x coordinate of point A−0lope = \frac{y\, coordinate\, of\, point\, A -0}{x\, coordinate\, of\, point\, A -0}

STEP 6

implify the above expression to getlope=y coordinate of point Ax coordinate of point Alope = \frac{y\, coordinate\, of\, point\, A}{x\, coordinate\, of\, point\, A}

STEP 7

Comparing the expressions for average speed and slope, we see that they are the same. Therefore, the average speed of the cat is represented by the slope of the line through AA and (0,0)(0,0).
The correct option is Slope of line through AA and (0,0)(0,0).

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