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.
debis walk around the mall

laps	steps
1	4,300
2	6,725
3	9,150
4	11,575

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 2,425 steps.
• one lap around the mall is equal to 4,300 steps.
• debi walks 6,175 steps per lap around the mall.

Explanation:

Step1: Analyze the table data

We have the number of steps for different laps. When laps = 0, steps = 1875 (this is the initial steps, maybe before starting to walk laps). When laps = 1, steps = 4300. To find the steps per lap, we calculate the difference between steps at lap 1 and lap 0.

Step2: Calculate steps per lap

Steps per lap = Steps at lap 1 - Steps at lap 0 = \(4300 - 1875 = 2425\)? Wait, no, wait. Wait, let's check the difference between consecutive laps. From lap 1 to lap 2: \(6725 - 4300 = 2425\). From lap 2 to lap 3: \(9150 - 6725 = 2425\). From lap 3 to lap 4: \(11575 - 9150 = 2425\). So the number of steps per lap is 2425? Wait, but let's check the options. Wait, the first option says 1875 per lap, but that's the initial steps. Wait, the question is about the graph of the line representing the data. Let's model the data as a linear function. Let \(y\) be steps, \(x\) be laps. The equation is \(y = mx + b\), where \(b\) is the y - intercept (when \(x = 0\), \(y = 1875\)), and \(m\) is the slope (steps per lap). We can calculate \(m\) using two points, say \((0,1875)\) and \((1,4300)\). The slope \(m=\frac{4300 - 1875}{1 - 0}=\frac{2425}{1}=2425\)? Wait, no, wait the options: "One lap around the mall is equal to 2,425 steps." Wait, but let's re - examine. Wait, when laps = 0, steps = 1875 (maybe she had 1875 steps before starting to walk laps). Then, for each lap, she adds 2425 steps? Wait, no, the difference between lap 0 and lap 1 is \(4300 - 1875 = 2425\), lap 1 to lap 2 is \(6725 - 4300 = 2425\), etc. So the number of steps per lap is 2425? Wait, but the options: "One lap around the mall is equal to 2,425 steps." Wait, but let's check the first option: "Debi walks 1,875 steps per lap around the mall." But 1875 is the steps at lap 0. The second option: "One lap around the mall is equal to 2,425 steps." Let's verify with the data. From lap 0 (1875 steps) to lap 1 (4300 steps), the increase is \(4300 - 1875 = 2425\) steps. So that means one lap (from 0 to 1 lap) is 2425 steps? Wait, no, maybe the initial 1875 steps are not part of the lap - walking. Wait, maybe the "one lap" is the number of steps added per lap. Wait, let's check the difference between steps for each lap. From 0 to 1 lap: \(4300 - 1875 = 2425\). From 1 to 2: \(6725 - 4300 = 2425\). From 2 to 3: \(9150 - 6725 = 2425\). From 3 to 4: \(11575 - 9150 = 2425\). So the number of steps per lap (the rate of change) is 2425. Wait, but the option "One lap around the mall is equal to 2,425 steps" is correct? Wait, no, wait the first option: "Debi walks 1,875 steps per lap" is wrong because 1875 is the steps at 0 laps. The third option: "One lap around the mall is equal to 4,300 steps" is wrong because 4300 is steps at 1 lap (including the initial 1875). The fourth option: "Debi walks 6,175 steps per lap" is wrong. Wait, but wait, maybe I made a mistake. Wait, let's calculate the slope again. The slope \(m\) of the line \(y = mx + b\) is the number of steps per lap. Using points \((0,1875)\) and \((1,4300)\), \(m=\frac{4300 - 1875}{1 - 0}=2425\). So the number of steps per lap is 2425, which means one lap around the mall is equal to 2,425 steps. Wait, but let's check the options again. The second option is "One lap around the mall is equal to 2,425 steps." Wait, but let's confirm with the data. When she walks 1 lap (from 0 to 1 lap), the number of steps she walks for that lap is \(4300 - 1875 = 2425\). So that's the number of steps per lap. So the correct statement is "One lap around the mall is equal to 2,425 steps." Wait, but wait, the first option: "Debi walks 1,875 steps per lap" is the y - intercept, not the steps per lap. The third option: 4300 is the total steps at 1 lap (including initial), not per lap. The fourth option: 6175 is not the difference. So the correct option is the second one? Wait, no, wait I think I messed up. Wait, let's recalculate:

Wait, when laps = 0, steps = 1875.

When laps = 1, steps = 4300. So the number of steps for 1 lap is \(4300 - 1875=2425\).

When laps = 2, steps = 6725. Steps for the second lap: \(6725 - 4300 = 2425\).

So each lap is 2425 steps. So the statement "One lap around the mall is equal to 2,425 steps" is true.

Answer:

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