Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.

The point on the graph shows his
arrival at the bumper cars. What do
the coordinates of the point tell us
about the situation?

What does the point (0,0) mean in
this situation?

What is the constant of
proportionality for the relationship
between time and distance? What
does it tell you about Tyler's walk?
Where do you see it in the graph?

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  a) It took 40 seconds to go 50 meters from the ticket booth

  b) Tyler started at the ticket booth

  c) k = 5/4

  d) Tyler walked at the rate of 1.25 meters per second

  e) The constant of proportionality is the slope of the line from (0, 0) to (40, 50). It is not shown on the graph.

Step-by-step explanation:

a) The axis labels on the graph tell you that 40 represents the number of seconds of elapsed time, and 50 represents the number of meters from the ticket booth. With the information in the problem statement, the coordinates (40, 50) tell us it took Tyler 40 seconds to walk 50 meters from the ticket booth to the bumper cars.

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b) The point (0, 0) tells us that Tyler started counting time when he left the ticket booth.

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c) The constant of proportionality is the ratio of the second coordinate to the first. The constant of proportionality is 50/40 = 5/4 = 1.25. (Its units are meters per second.)

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d) The constant of proportionality tells us that Tyler's steady pace was 1.25 meters per second.

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e) The constant of proportionality is not shown on the graph. It is the slope of a line between the origin and the point (40, 50).

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer