In this video, we are graphing how high up the head is from the ground in inches when going up and down the staircase at different speeds. While crossing, every so often the person would stop along the stairs, creating different coordinate points (ordered pairs) when graphing the height of the head.
My partners and I collected our data by measuring :
- NUMBER OF STAIRS = 14 on each side
- HEIGHT OF EACH STEP = 6.5 inches
- LENGTH OF EACH STEP = 11.5 inches
- LENGTH OF ENTIRE STAIRCASE = 495 inches
- HEIGHT OF PERSON = 49.2 inches
After watching the video, we concluded :
The ordered pair coordinates were based off of time in seconds (independent variable-x) and height of the head in inches (dependent variable-y).
We calculated our outputs by..
- (0 seconds) 0 steps + 49.2 head height = 49.2 inches
- (10 seconds) 5 steps x 6.5 inches + 49.2 head height = 82 inches
- (17 seconds) 12 steps x 6.5 inches + 49.2 head height = 127 inches
- (24 seconds) 14 steps x 6.5 inches + 49.2 head height = 140 inches
- (31 seconds) 9 steps x 6.5 inches + 49.2 head height = 108 inches
- (37 seconds) 3 steps x 6.5 inches + 49.2 head height = 69 inches
- (42 seconds) 0 steps + 49.2 head height = 49.2 inches
Our graph, titled : Across the Staircase represents the coordinate points from the table of values. The graph displays the amount of time it took to get from the start to the end, and the periods of time that the person stopped to take a break. This created a combination of horizontal and vertical lines. The y-axis goes up by 10 inches, and the x-axis goes up by 2 seconds.
- The graph is continuous – in between numbers (decimals) are alright because time and height can have many values, they are not only whole values.
- It is a function (used the vertical line test – no graphed line is crossed twice).
- Non-linear graph – the line is not a constant straight line, it changes its slope after each point.
- Between the points (0,50) and (10,81), the rate of change is 3.1 inches/seconds. -> 81-50 ÷ 10-0 = 3.1
- The rate in our graph changes throughout our video. It is caused by the speed the person is moving across the staircase and the length of time the person stops to take breaks.
Fantastic work, Dani. You’ve demonstrated a thorough understanding of interpreting, graphing, and analyzing a relation. Your description of the activity is clear, and the graph is clearly labeled. I like the added diagram of the event, a nice touch! Blog post shows care and attention to detail.