debi walks laps around the mall for exercise during the winter months. the table represents the number of…

Explanation:

Step 1: Find the slope (steps per lap)

The slope ( m ) of a line through two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Let's take ( (0, 1875) ) and ( (1, 4300) ). Then ( m=\frac{4300 - 1875}{1 - 0}=\frac{2425}{1}=2425 )? Wait, no, wait. Wait, when ( x = 0 ), steps are 1875 (that's the y - intercept, initial steps maybe). Let's check the difference between steps for each lap. From lap 0 to lap 1: ( 4300 - 1875 = 2425 )? Wait, no, wait the table: Laps 0: 1875, Laps 1: 4300, Laps 2: 6725, Laps 3: 9150, Laps 4: 11575. Let's calculate the difference between consecutive steps: ( 4300 - 1875 = 2425 ), ( 6725 - 4300 = 2425 ), ( 9150 - 6725 = 2425 ), ( 11575 - 9150 = 2425 ). Wait, but the first option says 1875 steps per lap, second says one lap is 2425 steps? Wait, no, wait the slope is the number of steps per lap. Wait, when laps increase by 1, steps increase by 2425? Wait, no, wait at lap 0, steps are 1875. So the equation of the line is ( y=mx + b ), where ( b = 1875 ) (when ( x = 0 ), ( y = 1875 )). Then for ( x = 1 ), ( y=4300 ), so ( 4300=m(1)+1875 ), so ( m = 4300 - 1875=2425 ). Wait, but the first option is "Debi walks 1,875 steps per lap around the mall" – no, because when she does 1 lap, the steps increase by 2425 (from 1875 to 4300 is 2425 steps for 1 lap). Wait, wait maybe I misread. Wait the first option: "Debi walks 1,875 steps per lap" – but when laps go from 0 to 1, steps go from 1875 to 4300, so the number of steps per lap is ( 4300 - 1875 = 2425 )? Wait no, maybe the 1875 is the initial steps (when she has done 0 laps, maybe she has some steps from before? No, probably the line is a linear model where ( y ) is steps, ( x ) is laps. So the slope is steps per lap. Let's recalculate the slope between ( (0, 1875) ) and ( (1, 4300) ): ( m=\frac{4300 - 1875}{1 - 0}=2425 ). Between ( (1, 4300) ) and ( (2, 6725) ): ( \frac{6725 - 4300}{2 - 1}=2425 ). So the slope is 2425 steps per lap. Wait, but the options: first option: 1875 steps per lap – no. Second option: "One lap around the mall is equal to 2,425 steps" – that would be the slope, since each lap adds 2425 steps. Wait, but let's check the first option: if she walked 1875 steps per lap, then at lap 1, steps would be ( 1875\times1=1875 ), but the table says 4300. So that's wrong. Second option: one lap is 2425 steps. Let's see: 1875 (initial) + 2425 (lap 1) = 4300, which matches. Lap 2: 4300 + 2425 = 6725, which matches. So that's correct. Third option: one lap is 4300 steps? No, because lap 1 is 4300, but lap 2 is 6725, which is 4300 + 2425, so not 4300 per lap. Fourth option: 6175 steps per lap? No, because 1875 + 6175 = 8050, which is not 4300. So the correct statement is "One lap around the mall is equal to 2,425 steps." Wait, but let's check the options again. Wait the options are:

• 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.

Wait, maybe I made a mistake. Wait the slope is the rate of change, which is steps per lap. So the change in steps over change in laps. From lap 0 to lap 1: steps change from 1875 to 4300, so change in steps is ( 4300 - 1875 = 2425 ), change in laps is ( 1 - 0 = 1 ), so rate is 2425 steps per lap. So the second option says "One lap around the mall is equal to 2,425 steps" – that's the rate, so that's correct. The first option: 1875 is the y - intercept (when laps = 0, steps = 1875), not steps per lap. So the correct statement is the second one.

Answer:

The true statement is: One lap around the mall is equal to 2,425 steps. (Corresponding to the option: One lap around the mall is equal to 2,425 steps.)