Question

Debi walks laps around the mall for exercise during the winter months. The table represents the number of steps recorded on her pedometer as she walks laps around the mall one day.
Which statement is true about the graph of the line representing Debi’s data?
- Debi walks 1,875 steps per lap around the mall.
- One lap around the mall is equal to about 2,425 steps.
- One lap around the mall is equal to 4,300 steps.
- Debi walks 6,175 steps per lap around the mall.

Laps
0
1
2
3
4

Steps
1,875
4,300
6,725
9,150
11,575

Answer 1

The difference between the number of steps for a given (non-zero) number of laps and the number of steps for one less lap is 2425. The appropriate choice is ...

... One lap around the mall is equal to about 2,425 steps

Answer 2

Answer: second option. One lap around the mall is equal to about 2,425 steps

Explanation:

1) Show the data in an ordered form:

Laps     Steps

0            1,875

1             4,300

3            6,725

4            9,150

5            11,575

2) The question states that the graph representing Debi’s data is a line. That means that i)  the graph has a constant slope, and ii) the slope - intercept form of the equation that represents it is y = mx + b, where:

• y is the dependent variable: number of steps
• x is the independent variable: number of laps
• b is the y-intercept (value of y when x = 0)
• m is the slope (constant).

        m = run / rise = change in y / change in x

3) Find the slope for some pairs of values:

• m = [ 4,300 - 1,875] steps / [1 - 0]  laps =  2,425 steps/laps
• m = [6,725 - 4,300]  steps / [2 - 1] laps = 2,425 steps / laps
• you will obtain the same for every pair of poins, m = 2,425 steps / laps

4) The meaning of the slope is the number of steps per one lap around the mall. Hence the answer is the second option: One lap around the mall is equal to about 2,425 steps