Kaitlin is driving laps around a race track. The table below shows the relationship between the distance D (in kilometers) and the number of laps L that Kaitlin has driven.
Number of laps 1 2 3 4
Distance
(kilometers) 5 12 18 24
(a)For the information in the table, write an equation to represent the relationship between D and L.
(b)Choose the correct statement to represent this relationship.
Kaitlin is driving 1 kilometer per 6 laps.
Kaitlin is driving 1/6 kilometers per lap.
Kaitlin is driving 6 kilometers per lap.
Kaitlin is driving 1 kilometer per lap.
(a) To represent the relationship between D (distance) and L (number of laps), we can see that the distance increases by 7 kilometers for each additional lap. Therefore, we can represent this relationship with the equation D = 7L.
(b) The correct statement to represent this relationship is: Kaitlin is driving 7 kilometers per lap.
(a) To write an equation to represent the relationship between D (distance) and L (number of laps), we can observe that the distance increases by 7 kilometers with each additional lap. Additionally, when Kaitlin hasn't completed any laps, she hasn't covered any distance. We can use this information to write the equation:
D = 7L
(b) The correct statement to represent this relationship is:
Kaitlin is driving 7 kilometers per lap.
(a) To find the equation to represent the relationship between D (distance) and L (number of laps), we need to look for a pattern in the table.
From the table, we can see that as the number of laps increases, the distance also increases. The relationship appears to be linear.
One way to find the equation is to determine the slope of the line. We can calculate the change in distance (ΔD) divided by the change in laps (ΔL) for any two points in the table. Let's take the first two points (1 lap, 5 kilometers) and (2 laps, 12 kilometers).
ΔD = 12 - 5 = 7 kilometers
ΔL = 2 - 1 = 1 lap
The slope of the line is ΔD/ΔL = 7/1 = 7.
Now that we have the slope, we can use the point-slope form of a linear equation:
D - D1 = m(L - L1)
Where D1 and L1 are the coordinates of any point on the line and m is the slope. Let's use the first point (1 lap, 5 kilometers):
D - 5 = 7(L - 1)
Simplifying the equation:
D - 5 = 7L - 7
(b) The correct statement to represent this relationship is:
Kaitlin is driving 1 kilometer per lap.