Question

example 5

1. elevator the height of an elevator above the ground is given in the table.

interpret the meaning of the axes, scale, and origin of the corresponding graph
of the data.

Explanation:

Step1: Analyze the axes

The \(x -\)axis represents the height of the elevator (in feet), and the \(y -\)axis represents the time (in seconds).

Step2: Analyze the origin

The origin \((0,0)\) means that at time \(t = 0\) seconds, the height of the elevator \(h=0\) feet (i.e., at ground level).

Step3: Analyze the scale

For the height ( \(x -\)axis): Each unit (small - grid) represents \(10\) feet (since from \(0\) to \(20\) is \(2\) units, \(20\div2 = 10\)). For the time ( \(y -\)axis): Each unit (small - grid) represents \(1\) second (since from \(0\) to \(2\) is \(2\) units, \(2\div2=1\)).

Step4: Analyze the data trend

As time increases, the height of the elevator increases. The relationship between time and height is linear. We can find the rate of change (speed). Using the formula \(m=\frac{\Delta h}{\Delta t}\). Take two points \((0,0)\) and \((4,80)\). The slope \(m=\frac{80 - 0}{4-0}=20\) feet per second. This means the elevator is rising at a speed of \(20\) feet per second.

Answer:

The \(x -\)axis represents the height of the elevator (in feet), the \(y -\)axis represents the time (in seconds). The origin \((0,0)\) means the elevator is at ground level at \(t = 0\) seconds. The scale for the \(x -\)axis: each small - grid is \(10\) feet; for the \(y -\)axis: each small - grid is \(1\) second. The elevator is rising at a rate of \(20\) feet per second (calculated as \(\frac{80 - 0}{4-0}\)).