Question

a company rents accessible bikes for people with physical disabilities. the scatter plot shows the relationship between the number of hours an accessible bike is rented and the total amount paid at rental locations in different cities. is the line $y = 10x$ a good fit for the data? use the drop - down menus to explain. (the scatter plot titled accessible bike rentals has number of hours rented on the x - axis (ranging from 0 to 10) and total amount paid ($) on the y - axis (ranging from 0 to 100). there are data points plotted on the graph.)

Explanation:

Step1: Analyze the line \( y = 10x \)

For a line \( y = 10x \), when \( x = 1 \), \( y = 10(1)=10 \); \( x = 2 \), \( y = 20 \); \( x = 3 \), \( y = 30 \); \( x = 4 \), \( y = 40 \); \( x = 5 \), \( y = 50 \); \( x = 6 \), \( y = 60 \); \( x = 8 \), \( y = 80 \).

Step2: Compare with scatter plot points

• At \( x = 1 \), data points are around 10 - 30 (but most near 10? Wait, no, the plot: at \( x = 1 \), points are ~10 - 30? Wait, looking at the plot: \( x=1 \): points around 10 - 30? Wait, no, the y - axis is total amount paid. Let's check key points:
• For \( x = 6 \), the data point is 80. \( y = 10(6)=60 \), but the data point is 80, which is above 60.
• For \( x = 8 \), data point is 80, \( y = 10(8)=80 \) (matches here).
• For \( x = 2 \), data point is 60, \( y = 10(2)=20 \) (way below).
• For \( x = 4 \), data point is ~55, \( y = 10(4)=40 \) (below).
• For \( x = 5 \), data point is ~55, \( y = 10(5)=50 \) (close but not exact).
• The line \( y = 10x \) doesn't pass through or be close to most of the data points. The data points are generally above the line for higher \( x \) (except \( x = 8 \)) and some below for lower \( x \), but the overall trend: let's see the general trend of the data. The data seems to have a positive correlation, but the line \( y = 10x \) doesn't fit well because most points are not close to it. For example, at \( x = 2 \), the data point is 60, but \( y = 10x \) gives 20, a big difference. At \( x = 4 \), data is ~55, line gives 40. At \( x = 6 \), data is 80, line gives 60. So the line \( y = 10x \) is not a good fit because the data points are not close to the line (most are far from it).

Answer:

No, the line \( y = 10x \) is not a good fit for the data because most of the data points in the scatter plot are not close to the line \( y = 10x \) (e.g., at \( x = 2 \), the data point is around 60 while \( y = 10x \) gives 20; at \( x = 4 \), data is around 55 while \( y = 10x \) gives 40; at \( x = 6 \), data is 80 while \( y = 10x \) gives 60, showing significant deviations).